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Can one recognize a function from its graph? 我们能从一个函数的图形中认出它吗?
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-30 DOI: 10.4171/zaa/1730
Jürgen Appell, Agnieszka Chlebowicz, Simon Reinwand, Beata Rzepka
We analyse the “interplay” between analytical properties of a real function on a metric space, on the one hand, and topological properties of its graph, on the other. In particular, we study functions with closed, compact, connected, pathwise connected, or locally connected graphs, and we give nine conditions on the graph which are equivalent to the continuity of a function. A main emphasis is put on examples and counterexamples which illustrate how significant our hypotheses are, and how far sufficient conditions are from being necessary.
我们分析度量空间上实函数的解析性质与图的拓扑性质之间的“相互作用”。特别地,我们研究了具有闭图、紧图、连通图、路径连通图和局部连通图的函数,并给出了图上等价于函数连续性的9个条件。主要的重点放在例子和反例子上,这些例子说明了我们的假设是多么重要,以及充分条件离必要条件有多远。
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引用次数: 0
Sign changing solutions for critical double phase problems with variable exponent 变指数临界双相问题的变符号解
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-30 DOI: 10.4171/zaa/1731
Nikolaos S. Papageorgiou, Francesca Vetro, Patrick Winkert
In this paper, we deal with a double phase problem with variable exponent and a right-hand side consisting of a Carathéodory perturbation defined only locally and of a critical term. We stress that the presence of the critical term inhibits the possibility to apply results of the critical point theory to the corresponding energy functional. Instead, we use suitable cut-off functions and truncation techniques in order to work with a coercive functional. Then, using variational tools and an appropriate auxiliary coercive problem, we can produce a sequence of sign changing solutions to our main problem converging to $0$ in $L^{infty}$ and in the Musielakk–Orlicz Sobolev space.
本文研究了一类变指数双相问题,该问题的右侧包含一个仅局部定义的临界项的carathacimodory摄动。我们强调,临界项的存在抑制了将临界点理论的结果应用于相应能量泛函的可能性。相反,我们使用合适的截止函数和截断技术来处理强制泛函。然后,使用变分工具和适当的辅助强制问题,我们可以产生一系列的变号解,我们的主要问题收敛到$L^{infty}$和Musielakk-Orlicz Sobolev空间中的$0$。
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引用次数: 0
Global structure of positive solutions for a fourth-order boundary value problem with singular data 一类具有奇异数据的四阶边值问题正解的全局结构
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-30 DOI: 10.4171/zaa/1729
Ruyun Ma, Zhongzi Zhao, Mantang Ma
We are concerned with a problem described the deformation of a simply supported beam of the form $$ u^{(4)}(x)+c(x)u(x) + sum^p_{i=1}c_idelta(x-x_i)u(x) = lambda a(u(x)) + lambdasum^q_{j=1}a_j(u(x))delta(x-y_j), quad xin (0,1), $$ $$ u(0)=u(1)=u''(0)=u''(1)=0, $$ where $lambda$ is a positive parameter, $cin C([0, 1],mathbb{R})$, $c_i in mathbb{R}$, $a, a_jin C([0,infty),[0,infty))$, $i = 1, 2, ldots, p$, $j= 1, 2, ldots, q$, $p, q in mathbb{N}$. The Dirac delta impulses $delta = delta(x)$ are applied at given points $0 < x_1 < x_2
我们关注的是形式为$$ u^{(4)}(x)+c(x)u(x) + sum^p_{i=1}c_idelta(x-x_i)u(x) = lambda a(u(x)) + lambdasum^q_{j=1}a_j(u(x))delta(x-y_j), quad xin (0,1), $$$$ u(0)=u(1)=u''(0)=u''(1)=0, $$的简支梁的变形问题,其中$lambda$是一个正参数,$cin C([0, 1],mathbb{R})$, $c_i in mathbb{R}$, $a, a_jin C([0,infty),[0,infty))$, $i = 1, 2, ldots, p$, $j= 1, 2, ldots, q$, $p, q in mathbb{N}$。狄拉克脉冲$delta = delta(x)$应用于给定点$0 < x_1 < x_2
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引用次数: 0
Integrability for Hardy operators of double phase 双相Hardy算子的可积性
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-30 DOI: 10.4171/zaa/1732
Yoshihiro Mizuta, Tetsu Shimomura
We establish Hardy–Sobolev and Hardy–Trudinger inequalities in weighted Orlicz spaces on $mathbb{R}^n$. As an application, we prove Hardy–Sobolev and Hardy–Trudinger inequalities in the framework of general double phase functionals given by $$ varphi_p(x,t) = varphi_1(t^p) + varphi_2((b(x)t)^p), quad xin mathbb{R}^n,, t ge 0, $$ where $p>1$, $varphi_1, varphi_2$ are positive convex functions on $(0,infty)$ and $b$ is a non-negative function on $[0,infty)$ which is Hölder continuous of order $theta in (0,1]$.
在$mathbb{R}^n$上建立了加权Orlicz空间中的Hardy-Sobolev不等式和Hardy-Trudinger不等式。作为应用,我们在$$ varphi_p(x,t) = varphi_1(t^p) + varphi_2((b(x)t)^p), quad xin mathbb{R}^n,, t ge 0, $$给出的一般双相泛函的框架内证明了Hardy-Sobolev和Hardy-Trudinger不等式,其中$p>1$、$varphi_1, varphi_2$是$(0,infty)$上的正凸函数,$b$是$[0,infty)$上的非负函数,它是Hölder阶$theta in (0,1]$连续的。
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引用次数: 0
Cocompact embedding theorem for functions of bounded variation into Lorentz spaces 有界变分函数在洛伦兹空间中的紧嵌入定理
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-13 DOI: 10.4171/zaa/1728
Lin Zhao
We show that the embedding $dot{mathrm{BV}}(mathbb{R}^N)hookrightarrow L^{1^ast,q}(mathbb{R}^N)$, $q>1$ is cocompact with respect to the group and the profile decomposition for $dot{mathrm{BV}}(mathbb{R}^N)$. This paper extends the cocompactness and profile decomposition for the critical space $L^{1^ast}(mathbb{R}^N)$ to Lorentz spaces $L^{1^ast,q}(mathbb{R}^N)$, $q>1$. A~counterexample for $dot{mathrm{BV}}(mathbb{R}^N)hookrightarrow L^{1^ast,1}(mathbb{R}^N)$ not cocompact is given in the last section.
我们证明了嵌入$dot{ mathm {BV}}(mathbb{R}^N)hookrightarrow L^{1^ast,q}(mathbb{R}^N)$, $q>1$对于群和$dot{ mathm {BV}}(mathbb{R}^N)$的剖分是紧的。本文将临界空间$L^{1^ ast}(mathbb{R}^N)$的紧性和轮廓分解推广到洛伦兹空间$L^{1^ ast,q}(mathbb{R}^N)$, $q>1$。$dot{ mathm {BV}}(mathbb{R}^N)hookrightarrow L^{1^ast,1}(mathbb{R}^N)$不紧的反例在最后一节给出。
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引用次数: 0
Real interpolations for martingale Hardy–Orlicz–Lorentz spaces 鞅Hardy-Orlicz-Lorentz空间的实插值
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-13 DOI: 10.4171/zaa/1726
Wenfei Fan, Yanmeng Li, Lian Wu
The purpose of this paper is to provide a new proof of real interpolations for martingale Hardy–Orlicz–Lorentz spaces. Different from the usual proof, our approach does not rely on any atomic decompositions. Instead, we establish the result via new Holmstedt’s formulae in martingale Hardy–Orlicz type spaces.
本文的目的是为鞅Hardy-Orlicz-Lorentz空间的实插值提供一个新的证明。与通常的证明不同,我们的方法不依赖于任何原子分解。相反,我们通过鞅Hardy-Orlicz型空间中的新Holmstedt公式来建立结果。
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引用次数: 0
Multi-layered tumor cell cultures with almost periodic nutrient supply 多层肿瘤细胞培养,几乎有周期性的营养供应
3区 数学 Q2 MATHEMATICS Pub Date : 2023-09-13 DOI: 10.4171/zaa/1727
Homero G. Díaz-Marín
Modeling of multi-layered cell cultures (MCC) assume flat geometry in a 3D tumor growth model.Some results available in the time-dependent framework assume a periodic nutrient supply $Phi(t)$. Our aim is to generalize such considerations. Namely, we show that a stable oscillating tumor growth arises in the long term, whenever the mean value of the almost periodic nutrient supply $overline{Phi}$ surpasses certain threshold level, $overline{Phi}>tilde{sigma}$. Meanwhile, a vanishing tumor is predicted in the complementary case, $overline{Phi}leq tilde{sigma}$.
多层细胞培养(MCC)的建模在三维肿瘤生长模型中假定为平面几何。在时间依赖框架中获得的一些结果假设有周期性的营养供应$Phi(t)$。我们的目的是概括这些考虑。也就是说,我们表明,只要几乎周期性的营养供应的平均值$overline{Phi}$超过一定的阈值$overline{Phi}>tilde{sigma}$,长期内就会出现稳定的振荡肿瘤生长。同时,在互补病例$overline{Phi}leq tilde{sigma}$中,预测肿瘤会消失。
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引用次数: 0
Fractional differentiability for elliptic double obstacle problems with measure data 具有测量数据的椭圆型双障碍问题的分数可微性
IF 1.2 3区 数学 Q2 MATHEMATICS Pub Date : 2023-07-10 DOI: 10.4171/zaa/1721
Sun-Sig Byun, Kyeong Song, Yeonghun Youn
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引用次数: 1
Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x); q(x))-Laplacian operator 涉及(p(x))的非线性粘弹性板方程解的整体存在性、渐近稳定性和爆破性问(x))拉普拉斯算符
IF 1.2 3区 数学 Q2 MATHEMATICS Pub Date : 2023-06-20 DOI: 10.4171/zaa/1722
M. Shahrouzi, J. Ferreira, F. Tahamtani
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引用次数: 1
On Korpelevich’s extragradient algorithm 关于Korpelevich的提取算法
IF 1.2 3区 数学 Q2 MATHEMATICS Pub Date : 2023-06-20 DOI: 10.4171/zaa/1724
Nicholas Pischke
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引用次数: 0
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