具有对数凹权值的退化p$ p$ -拉普拉斯型方程的二阶正则性

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-14 DOI:10.1112/jlms.70299

Carlo Alberto Antonini, Giulio Ciraolo, Francesco Pagliarin

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引用次数: 0

摘要

考虑凸域上具有齐次Neumann边界条件的加权p$ p$ -拉普拉斯型方程，其中权是一个可能在边界退化的对数凹函数。在有界域的情况下，我们提供了锐利的全局二阶估计。对于无界域，我们证明了边界处的局部估计。即使在p=2$ p=2$的情况下，结果也是新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Second-order regularity for degenerate

p
$p$
-Laplace type equations with log-concave weights

查看原文本刊更多论文

Second-order regularity for degenerate p $p$ -Laplace type equations with log-concave weights

We consider weighted $p$ -Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp global second-order estimates. For unbounded domains, we prove local estimates at the boundary. The results are new even for the case $p = 2$ .

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.