Journal of Functional Analysis最新文献

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A Campanato regularity theory for multi-valued functions with applications to minimal surface regularity theory

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110908

Paul Minter

The regularity theory of the Campanato space

L_{k}^{(q, λ)} (Ω)

has found many applications within the regularity theory of solutions to various geometric variational problems. Here we extend this theory from single-valued functions to multi-valued functions, adapting for the most part Campanato's original ideas ([4]). We also give an application of this theory within the regularity theory of stationary integral varifolds. More precisely, we prove a regularity theorem for certain blow-up classes of multi-valued functions, which typically arise when studying blow-ups of sequences of stationary integral varifolds converging to higher multiplicity planes or unions of half-planes. In such a setting, based in part on ideas in [16], [11], and [3], we are able to deduce a boundary regularity theory for multi-valued harmonic functions; such a boundary regularity result would appear to be the first of its kind for the multi-valued setting. In conjunction with [9], the results presented here establish a regularity theorem for stable codimension one stationary integral varifolds near classical cones of density

\frac{5}{2}

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引用次数: 0

Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110903

Eva A. Gallardo-Gutiérrez , F. Javier González-Doña

We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. Moreover, a large subclass consists of decomposable operators in the sense of Colojoară and Foiaş [3].

引用次数: 0

Minimal surface equation and Bernstein property on RCD spaces

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110907

Alessandro Cucinotta

We show that if

(X, d, m)

is an

RCD (K, N)

space and

u \in W_{l o c}^{1, 1} (X)

is a solution of the minimal surface equation, then u is harmonic on its graph (which has a natural metric measure space structure). If

K = 0

this allows to obtain an Harnack inequality for u, which in turn implies the Bernstein property, meaning that any positive solution to the minimal surface equation must be constant. As an application, we obtain oscillation estimates and a Bernstein Theorem for minimal graphs in products

M \times R

, where

M

is a smooth manifold (possibly weighted and with boundary) with non-negative Ricci curvature.

引用次数: 0

A characterisation of the Daugavet property in spaces of vector-valued Lipschitz functions

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110896

Rubén Medina , Abraham Rueda Zoca

Let M be a metric space and X be a Banach space. In this paper we address several questions about the structure of

F (M) {\hat{\otimes}}_{π} X

and

{Lip}_{0} (M, X)

. Our results are the following:

(1)
We prove that if M is a length metric space then ${Lip}_{0} (M, X)$ has the Daugavet property. As a consequence, if M is length we obtain that $F (M) {\hat{\otimes}}_{π} X$ has the Daugavet property. This gives an affirmative answer to [9, Question 1] (also asked in [16, Remark 3.8]).
(2)
We prove that if M is a non-uniformly discrete metric space or an unbounded metric space then the norm of $F (M) {\hat{\otimes}}_{π} X$ is octahedral, which solves [4, Question 3.2 (1)].
(3)
We characterise all the Banach spaces X such that $L (X, Y)$ is octahedral for every Banach space Y, which solves a question by Johann Langemets.

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引用次数: 0

On a kinetic Poincaré inequality and beyond

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110899

Lukas Niebel , Rico Zacher

In this article, we give a trajectorial proof of a kinetic Poincaré inequality which plays an important role in the De Giorgi-Nash-Moser theory for kinetic equations. The present work improves a result due to J. Guerand and C. Mouhot [12] in several directions. We use kinetic trajectories along the vector fields

\partial_{t} + v \cdot \nabla_{x}

and

\partial_{v_{i}}

i = 1, \dots, d

and do not rely on higher-order commutators such as

[\partial_{v_{i}}, \partial_{t} + v \cdot \nabla_{x}] = \partial_{x_{i}}

or on the fundamental solution. The presented method also applies to more general hypoelliptic equations. We illustrate this by investigating a Kolmogorov equation with k steps.

引用次数: 0

Schauder-type estimates for fully nonlinear degenerate elliptic equations

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110900

Thialita M. Nascimento

In this paper, we examine regularity estimates for solutions to fully nonlinear, degenerated elliptic equations, at interior vanishing source points. By means of a geometric approach, we obtain, at such points, Schauder-type regularity estimates, which depend on the Hölder-like source-ellipticity vanishing rate.

引用次数: 0

Stability of abstract coupled systems

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-03-03 DOI: 10.1016/j.jfa.2025.110909

Serge Nicaise , Lassi Paunonen , David Seifert

We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting properties of the components, which are typically much simpler to analyse. As our main results we establish resolvent estimates and decay rates for abstract boundary-coupled systems. We illustrate the power of the general results by using them to obtain rates of energy decay in coupled systems of one-dimensional wave and heat equations, and in a multi-dimensional wave equation with an acoustic boundary condition.

引用次数: 0

The asymptotic stability on the line of ground states of the pure power NLS with 0 < |p − 3| ≪ 1

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-02-11 DOI: 10.1016/j.jfa.2025.110861

Scipio Cuccagna , Masaya Maeda

For exponents p satisfying

0 < | p - 3 | ≪ 1

and only in the context of spatially even solutions we prove that the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent p in the line are asymptotically stable. The proof is similar to a related result of Martel [45] for a cubic quintic NLS. Here we modify the second part of Martel's argument, replacing the second virial inequality for a transformed problem with a smoothing estimate on the initial problem, appropriately tamed by multiplying the initial variables and equations by a cutoff.

引用次数: 0

Upper bounds for solutions of Leibenson's equation on Riemannian manifolds

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-02-11 DOI: 10.1016/j.jfa.2025.110878

Alexander Grigor'yan, Philipp Sürig

We consider on Riemannian manifolds the Leibenson equation

\partial_{t} u = Δ_{p} u^{q}

that is also known as a doubly nonlinear evolution equation. We prove upper estimates of weak subsolutions to this equation on Riemannian manifolds with non-negative Ricci curvature in the case when p and q satisfy the conditions

1 < p < 2 and 1 \leq q < \frac{1}{p - 1} .

We show that these estimates are optimal in terms of long time behavior and near-optimal in terms of long distance behavior.

引用次数: 0

Littlewood-type theorems for random Dirichlet multipliers

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis

Pub Date : 2025-02-11 DOI: 10.1016/j.jfa.2025.110851

Guozheng Cheng , Xiang Fang , Chao Liu , Yufeng Lu

<div><div>In this paper we present a systematic study of random Dirichlet functions. In 1993, Cochran-Shapiro-Ullrich proved the following elegant result on random Dirichlet multipliers [21]: For any <math><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∈</mo><mi>D</mi></math>, the Dirichlet space over the unit disk, almost all of its randomizations<math><mo>(</mo><mi>R</mi><mi>f</mi><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mo>±</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup></math> are multipliers of <math><mi>D</mi></math>. The purpose of this paper is to exploit this result and to extend it in three directions, inspired by the 1930 theorem of Littlewood on random Hardy functions:<ul><li>(A)<div>We introduce a symbol space <math><msub><mrow><mi>M</mi></mrow><mrow><mo>⋆</mo></mrow></msub></math> for random multipliers on <math><mi>D</mi></math> and reformulate (and strengthen) the problem as the characterization of <math><msub><mrow><mi>M</mi></mrow><mrow><mo>⋆</mo></mrow></msub></math>. We then characterize <math><msub><mrow><mo>(</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><mrow><mo>⋆</mo></mrow></msub></math> for all <math><mi>p</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo><mi>α</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math> when <math><mi>α</mi><mo>≠</mo><mi>p</mi><mo>−</mo><mn>1</mn></math> (Theorem 55). The case <math><mi>p</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>α</mi><mo>=</mo><mn>0</mn></math> recovers the 1993 result.</div></li><li>(B)<div>We obtain a two-parameter version by formulating and solving a Littlewood-type problem for all <math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo><mo>∈</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math> (Theorem 69). The case <math><mi>p</mi><mo>=</mo><mi>q</mi><mo>=</mo><mn>2</mn></math> recovers the 1993 result.</div></li><li>(C)<div>We consider <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math> and <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow><mrow><m

引用次数: 0

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