变指数集的poincar不等式和Neumann问题

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Mathematics in Engineering Pub Date : 2021-08-21 DOI:10.3934/mine.2022036

D. Cruz-Uribe, Michael Penrod, S. Rodney

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引用次数: 2

摘要

在较早的一篇论文中，Cruz-Uribe, Rodney和Rosta证明了加权poincar不等式与一类退化的$ p $-拉普拉斯算子相关的Neumann问题弱解的存在性之间的等价性。本文证明了变指数空间中的poincar不等式与退化的$ {p(\cdot)} $-拉普拉斯方程解之间的类似等价性，这是一个具有非标准生长条件的非线性椭圆方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Poincaré inequalities and Neumann problems for the variable exponent setting

In an earlier paper, Cruz-Uribe, Rodney and Rosta proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate $ p $-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate $ {p(\cdot)} $-Laplacian, a non-linear elliptic equation with nonstandard growth conditions.

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来源期刊

Mathematics in Engineering MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

12 weeks