Communications on Pure and Applied Mathematics最新文献

英文中文

Integral formulation of Klein–Gordon singular waveguides 克莱因-戈登奇异波导的积分公式

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-10-07 DOI: 10.1002/cpa.22227

Guillaume Bal, Jeremy Hoskins, Solomon Quinn, Manas Rachh

We consider the analysis of singular waveguides separating insulating phases in two‐space dimensions. The insulating domains are modeled by a massive Schrödinger equation and the singular waveguide by appropriate jump conditions along the one‐dimensional interface separating the insulators. We present an integral formulation of the problem and analyze its mathematical properties. We also implement a fast multipole and sweeping‐accelerated iterative algorithm for solving the integral equations, and demonstrate numerically the fast convergence of this method. Several numerical examples of solutions and scattering effects illustrate our theory.

我们考虑分析在二维空间中分隔绝缘相的奇异波导。绝缘域由大质量薛定谔方程建模，奇异波导由沿分隔绝缘体的一维界面的适当跃迁条件建模。我们提出了问题的积分公式，并分析了其数学特性。我们还实现了一种求解积分方程的快速多极和扫频加速迭代算法，并在数值上证明了这种方法的快速收敛性。几个求解和散射效应的数值示例说明了我们的理论。

引用次数: 0

On minimizers in the liquid drop model 关于液滴模型中的最小化

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-10-07 DOI: 10.1002/cpa.22229

Otis Chodosh, Ian Ruohoniemi

We prove that round balls of volume uniquely minimize in Gamow's liquid drop model.

我们证明，在伽莫夫液滴模型中，圆球的体积唯一最小。

引用次数: 0

On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates 关于二维重力波的波湍流理论，I：确定性能量估计

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-09-11 DOI: 10.1002/cpa.22224

Yu Deng, Alexandru D. Ionescu, Fabio Pusateri

Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation here is different since the water waves equations are quasilinear and solutions cannot be constructed by iteration of the Duhamel formula due to unavoidable derivative loss. This is the first of two papers in which we design a new strategy to address this issue. We investigate solutions of the gravity water waves system in two dimensions. In the irrotational case, this system can be reduced to an evolution equation on the one‐dimensional interface, which is a large torus of size . Our first main result is a deterministic energy inequality, which provides control of (possibly large) Sobolev norms of solutions for long times, under the condition that a certain ‐type norm is small. This energy inequality is of “quintic” type: if the norm is , then the increment of the high‐order energies is controlled for times of the order , consistent with the approximate quartic integrability of the system. In the second paper in this sequence, we will show how to use this energy estimate and a propagation of randomness argument to prove a probabilistic regularity result up to times of the order , in a suitable scaling regime relating and . For our second main result, we combine the quintic energy inequality with a bootstrap argument using a suitable ‐norm of Strichartz‐type to prove that deterministic solutions with Sobolev data of size are regular for times of the order . In particular, on the real line, solutions exist for times of order . This improves substantially on all the earlier extended lifespan results for 2D gravity water waves with small Sobolev data.

我们在本文中的目标是启动对波浪湍流的严格研究，并推导出水波模型的波动力方程（WKEs）。近年来，在半线性模型（如薛定谔方程或多维 KdV 型方程）的背景下，这一问题受到了广泛关注。然而，我们这里的情况有所不同，因为水波方程是准线性方程，由于不可避免的导数损失，无法通过迭代杜哈梅尔公式求解。本文是两篇论文中的第一篇，我们在其中设计了一种新策略来解决这一问题。我们研究了二维重力水波系统的解。在非旋转情况下，该系统可简化为一维界面上的演化方程，一维界面是一个大小为。我们的第一个主要结果是一个确定性能量不等式，它提供了对解的（可能很大的）Sobolev 准则的长时间控制，条件是某个 - 型准则很小。这种能量不等式属于 "五元 "类型：如果规范为，那么高阶能量的增量在阶次为，的时间内受到控制，这与系统的近似四元可整性是一致的。在本序列的第二篇论文中，我们将展示如何利用这一能量估计和随机性传播论证来证明一个概率正则性结果，在一个与和有关的合适的缩放机制中，直到次。对于我们的第二个主要结果，我们将五元能量不等式与使用合适的斯特里查兹类型-规范的自举论证相结合，证明具有索波列夫数据大小的确定性解在阶次为的时间内是正则的。特别是，在实线上，对于阶为 . 的时间，解是存在的。这大大改进了早先关于具有小索博列夫数据的二维重力水波的所有扩展寿命结果。

{"title":"On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates","authors":"Yu Deng, Alexandru D. Ionescu, Fabio Pusateri","doi":"10.1002/cpa.22224","DOIUrl":"https://doi.org/10.1002/cpa.22224","url":null,"abstract":"Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation here is different since the water waves equations are quasilinear and solutions cannot be constructed by iteration of the Duhamel formula due to unavoidable derivative loss. This is the first of two papers in which we design a new strategy to address this issue. We investigate solutions of the gravity water waves system in two dimensions. In the irrotational case, this system can be reduced to an evolution equation on the one‐dimensional interface, which is a large torus of size . Our first main result is a deterministic energy inequality, which provides control of (possibly large) Sobolev norms of solutions for long times, under the condition that a certain ‐type norm is small. This energy inequality is of “quintic” type: if the norm is , then the increment of the high‐order energies is controlled for times of the order , consistent with the approximate quartic integrability of the system. In the second paper in this sequence, we will show how to use this energy estimate and a propagation of randomness argument to prove a probabilistic regularity result up to times of the order , in a suitable scaling regime relating and . For our second main result, we combine the quintic energy inequality with a bootstrap argument using a suitable ‐norm of Strichartz‐type to prove that deterministic solutions with Sobolev data of size are regular for times of the order . In particular, on the real line, solutions exist for times of order . This improves substantially on all the earlier extended lifespan results for 2D gravity water waves with small Sobolev data.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"10 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142170872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Convergence to the planar interface for a nonlocal free-boundary evolution 收敛到非局部自由边界演化的平面界面

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-09-05 DOI: 10.1002/cpa.22225

Felix Otto, Richard Schubert, Maria G. Westdickenberg

We capture optimal decay for the Mullins–Sekerka evolution, a nonlocal, parabolic free boundary problem from materials science. Our main result establishes convergence of BV solutions to the planar profile in the physically relevant case of ambient space dimension three. Far from assuming small or well-prepared initial data, we allow for initial interfaces that do not have graph structure and are not connected, hence explicitly including the regime of Ostwald ripening. In terms only of initially finite (not small) excess mass and excess surface energy, we establish that the surface becomes a Lipschitz graph within a fixed timescale (quantitatively estimated) and remains trapped within this setting. To obtain the graph structure, we leverage regularity results from geometric measure theory. At the same time, we extend a duality method previously employed for one-dimensional PDE problems to higher dimensional, nonlocal geometric evolutions. Optimal algebraic decay rates of excess energy, dissipation, and graph height are obtained.

我们捕捉 Mullins-Sekerka 演化的最佳衰减，这是材料科学中的一个非局部抛物自由边界问题。我们的主要结果证明，在环境空间维数为三的物理相关情况下，BV 解收敛于平面轮廓。我们不假定初始数据较小或准备充分，而是允许初始界面不具有图形结构且不相连，因此明确包括奥斯特瓦尔德熟化机制。仅就初始有限（不小于）过剩质量和过剩表面能而言，我们确定表面在一个固定的时间尺度（定量估计）内成为一个 Lipschitz 图形，并在此环境中保持困顿。为了获得图结构，我们利用了几何度量理论的正则性结果。同时，我们将以前用于一维 PDE 问题的对偶方法扩展到了更高维度的非局部几何演化。我们获得了过剩能量、耗散和图高度的最佳代数衰减率。

引用次数: 0

Asymptotics of block Toeplitz determinants with piecewise continuous symbols 具有片断连续符号的块托普利兹行列式的渐近论

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-08-28 DOI: 10.1002/cpa.22223

Estelle Basor, Torsten Ehrhardt, Jani A. Virtanen

We determine the asymptotics of the block Toeplitz determinants $� � � det � �_{T � n �} � � (� ϕ �) � � � �$ as $� � � n � \to � \infty � � �$ for $� � � N � \times � N � � �$ matrix-valued piecewise continuous functions $� � ϕ � �$ with a finitely many jumps under mild additional conditions. In particular, we prove that

在温和的附加条件下，我们确定了块托普利兹行列式的渐近线，如同具有有限次跳跃的矩阵值片断连续函数。特别是，我们证明了，，和是取决于矩阵符号的常数，并在我们的主要结果中进行了描述。我们的方法基于托普利兹行列式的新局部定理、计算具有片断连续矩阵值符号的托普利兹算子的弗雷德霍姆指数的新方法以及其他算子理论方法。作为我们结果的一个应用，我们考虑了在量子自旋链模型的纠缠熵研究中出现的片断连续符号。

{"title":"Asymptotics of block Toeplitz determinants with piecewise continuous symbols","authors":"Estelle Basor, Torsten Ehrhardt, Jani A. Virtanen","doi":"10.1002/cpa.22223","DOIUrl":"10.1002/cpa.22223","url":null,"abstract":"We determine the asymptotics of the block Toeplitz determinants <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>det</mo>\u0000 <msub>\u0000 <mi>T</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>ϕ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$det T_n(phi)$</annotation>\u0000 </semantics></math> as <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math> for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>×</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$Ntimes N$</annotation>\u0000 </semantics></math> matrix-valued piecewise continuous functions <math>\u0000 <semantics>\u0000 <mi>ϕ</mi>\u0000 <annotation>$phi$</annotation>\u0000 </semantics></math> with a finitely many jumps under mild additional conditions. In particular, we prove that\u0000\u0000 ","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"120-160"},"PeriodicalIF":3.1,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22223","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142090102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tight Lipschitz hardness for optimizing mean field spin glasses 优化均值场自旋玻璃的严格 Lipschitz 硬度

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-08-20 DOI: 10.1002/cpa.22222

Brice Huang, Mark Sellke

We study the problem of algorithmically optimizing the Hamiltonian <math> <semantics> <msub> <mi>H</mi> <mi>N</mi> </msub> <annotation>$H_N$</annotation> </semantics></math> of a spherical or Ising mixed <math> <semantics> <mi>p</mi> <annotation>$p$</annotation> </semantics></math>-spin glass. The maximum asymptotic value <math> <semantics> <mi>OPT</mi> <annotation>${mathsf {OPT}}$</annotation> </semantics></math> of <math> <semantics> <mrow> <msub> <mi>H</mi> <mi>N</mi> </msub> <mo>/</mo> <mi>N</mi> </mrow> <annotation>$H_N/N$</annotation> </semantics></math> is characterized by a variational principle known as the Parisi formula, proved first by Talagrand and in more generality by Panchenko. Recently developed approximate message passing (AMP) algorithms efficiently optimize <math> <semantics> <mrow> <msub> <mi>H</mi> <mi>N</mi> </msub> <mo>/</mo> <mi>N</mi> </mrow> <annotation>$H_N/N$</annotation> </semantics></math> up to a value <math> <semantics> <mi>ALG</mi> <annotation>${mathsf {ALG}}$</annotation> </semantics></math> given by an extended Parisi formula, which minimizes over a larger space of functional order parameters. These two objectives are equal for spin glasses exhibiting a no overlap gap property (OGP). However, <math> <semantics> <mrow> <mi>ALG</mi> <mo><</mo> <mi>OPT</mi> </mrow> <annotation>${mathsf {ALG}}< {mathsf {OPT}}$</annotation> </semantics></math> can also occur, and no efficient algorithm producing an objective value exceeding <math> <semantics> <mi>ALG</mi> <annotation>${mathsf {ALG}}$</annotation> </semantics></math> is known. We prove that for mixed even <math> <semantics> <mi>p</mi> <annotation>$p$</annotation> </semantics></math>-spin models, no algorithm satisfying an overlap concentration property can produce an objective larger than <math> <semantics> <mi>ALG</mi> <annotation>${mathsf {ALG}}$</annotation> </semantics></math> with non-negligible probability.

我们研究了球面或伊辛混合 p $p$ -自旋玻璃的哈密顿H N $H_N$ 的算法优化问题。H N / N $H_N/N$ 的最大渐近值 OPT ${mathsf {OPT}}$ 是由一个称为帕里西公式的变分原理表征的。最近开发的近似消息传递（AMP）算法可以有效优化 H N / N $H_N/N$ 达到扩展帕里西公式给出的值 ALG ${mathsf {ALG}}$，该值在更大的功能阶参数空间上最小化。对于表现出无重叠间隙特性（OGP）的自旋玻璃来说，这两个目标是相等的。然而，ALG < OPT ${mathsf {ALG}}< {mathsf {OPT}}$ 也可能出现，而且目前还不知道哪种高效算法能产生超过 ALG ${mathsf {ALG}}$ 的目标值。我们证明，对于混合偶数 p $p$ -自旋模型，没有一种满足重叠集中特性的算法能以不可忽略的概率产生大于 ALG ${mathsf {ALG}}$的目标值。这一特性适用于所有对 H N $H_N$ 的无序系数具有适当 Lipschitz 依赖性的算法。它包括梯度下降、AMP 和朗格文动力学在有界时间内运行的自然公式，尤其包括上述实现 ALG ${mathsf {ALG}}$的算法。为了证明这一结果，我们将 Gamarnik 和 Sudan 引入的 OGP 框架大幅推广到任意超对称禁止解结构。

{"title":"Tight Lipschitz hardness for optimizing mean field spin glasses","authors":"Brice Huang, Mark Sellke","doi":"10.1002/cpa.22222","DOIUrl":"https://doi.org/10.1002/cpa.22222","url":null,"abstract":"We study the problem of algorithmically optimizing the Hamiltonian <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <annotation>$H_N$</annotation>\u0000 </semantics></math> of a spherical or Ising mixed <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-spin glass. The maximum asymptotic value <math>\u0000 <semantics>\u0000 <mi>OPT</mi>\u0000 <annotation>${mathsf {OPT}}$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$H_N/N$</annotation>\u0000 </semantics></math> is characterized by a variational principle known as the Parisi formula, proved first by Talagrand and in more generality by Panchenko. Recently developed approximate message passing (AMP) algorithms efficiently optimize <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>H</mi>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$H_N/N$</annotation>\u0000 </semantics></math> up to a value <math>\u0000 <semantics>\u0000 <mi>ALG</mi>\u0000 <annotation>${mathsf {ALG}}$</annotation>\u0000 </semantics></math> given by an extended Parisi formula, which minimizes over a larger space of functional order parameters. These two objectives are equal for spin glasses exhibiting a no overlap gap property (OGP). However, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ALG</mi>\u0000 <mo><</mo>\u0000 <mi>OPT</mi>\u0000 </mrow>\u0000 <annotation>${mathsf {ALG}}&lt; {mathsf {OPT}}$</annotation>\u0000 </semantics></math> can also occur, and no efficient algorithm producing an objective value exceeding <math>\u0000 <semantics>\u0000 <mi>ALG</mi>\u0000 <annotation>${mathsf {ALG}}$</annotation>\u0000 </semantics></math> is known. We prove that for mixed even <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-spin models, no algorithm satisfying an overlap concentration property can produce an objective larger than <math>\u0000 <semantics>\u0000 <mi>ALG</mi>\u0000 <annotation>${mathsf {ALG}}$</annotation>\u0000 </semantics></math> with non-negligible probability.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"60-119"},"PeriodicalIF":3.1,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global regularity for critical SQG in bounded domains 有界域中临界 SQG 的全局正则性

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-07-24 DOI: 10.1002/cpa.22221

Peter Constantin, Mihaela Ignatova, Quoc-Hung Nguyen

We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in $� � �^{R � 2 �} � �$ . We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.

我们证明了有界域中临界耗散 SQG 方程全局平稳解的存在性和唯一性。我们引入了一种新方法，将有界域中的单一非局部非线性演化方程转化为整个空间中的扩展非局部非线性演化方程的相互作用系统。然后利用扩展系统中的非局部算子的非线性最大原理方法进行证明。

引用次数: 0

A variational construction of Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities 具有孤立 Schoen-Wolfson 圆锥奇点的哈密顿静止面的变分构造

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-06-07 DOI: 10.1002/cpa.22220

Filippo Gaia, Gerard Orriols, Tristan Rivière

We construct using variational methods Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities. We obtain these surfaces through a convergence process reminiscent to the Ginzburg–Landau asymptotic analysis in the strongly repulsive regime introduced by Bethuel, Brezis and Hélein. We describe in particular how the prescription of Schoen–Wolfson conical singularities is related to optimal Wente constants.

我们利用变分法构建了具有孤立肖恩-沃尔夫森圆锥奇点的哈密顿静止曲面。我们通过一个收敛过程来获得这些表面，这个过程让人联想到 Bethuel、Brezis 和 Hélein 提出的强排斥机制中的金兹堡-兰道渐近分析。我们特别描述了舍恩-沃尔夫森锥奇点的处方与最佳温特常数之间的关系。

引用次数: 0

Almost sharp lower bound for the nodal volume of harmonic functions 谐函数节点体积的近似尖锐下界

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-05-29 DOI: 10.1002/cpa.22207

Alexander Logunov, Lakshmi Priya M. E., Andrea Sartori

This paper focuses on a relation between the growth of harmonic functions and the Hausdorff measure of their zero sets. Let $� � u � �$ be a real-valued harmonic function in $� � �^{R � n �} � �$ with $� � � u � (� 0 �) � = � 0 � � �$ and $� � � n � \geq � 3 � � �$ . We prove

本文主要研究谐函数的增长与其零集的 Hausdorff 度量之间的关系。设是一个实值谐函数，且。我们证明了翻倍指数是由定义的增长概念，这给出了、的零集的 Hausdorff 度量的一个近乎尖锐的下限，猜想它是线性的。文章的新内容是稳定增长的概念，以及谐函数倍指数分布下界的多尺度归纳技术。与之前最著名的下界，即纳迪拉什维利猜想相比，它给出了一个重大改进。

{"title":"Almost sharp lower bound for the nodal volume of harmonic functions","authors":"Alexander Logunov, Lakshmi Priya M. E., Andrea Sartori","doi":"10.1002/cpa.22207","DOIUrl":"10.1002/cpa.22207","url":null,"abstract":"This paper focuses on a relation between the growth of harmonic functions and the Hausdorff measure of their zero sets. Let <math>\u0000 <semantics>\u0000 <mi>u</mi>\u0000 <annotation>$u$</annotation>\u0000 </semantics></math> be a real-valued harmonic function in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$u(0)=0$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$nge 3$</annotation>\u0000 </semantics></math>. We prove\u0000\u0000 ","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 12","pages":"4328-4389"},"PeriodicalIF":3.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141177297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Allen–Cahn solutions with triple junction structure at infinity 无穷远处具有三重结点结构的艾伦-卡恩解

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2024-05-17 DOI: 10.1002/cpa.22204

Étienne Sandier, Peter Sternberg

We construct an entire solution $� � � U � : � �^{R � 2 �} � \to � �^{R � 2 �} � � �$ to the elliptic system

我们构建了一个椭圆系统的整体解，其中有一个 "三井 "势。这个解是相关能量的局部最小化，即在任何紧凑集合上，与该集合外的竞争者一致的能量最小化。此外，我们还证明，沿着子序列，"三井 "的 "井喷 "会逼近一个最小的 "三井"，即......。以前的结果假设了不同程度的势对称性，并没有建立局部最小性，但在这里我们不做这样的对称性假设。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Communications on Pure and Applied Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀