Local boundedness for $ p $-Laplacian with degenerate coefficients

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-09-13 DOI:10.3934/mine.2023081

P. Bella, Mathias Schaffner

引用次数: 0

Abstract

We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $ \nabla \cdot (\lambda |\nabla u|^{p-2}\nabla u) = 0 $, where the variable coefficient $ 0\leq\lambda $ and its inverse $ \lambda^{-1} $ are allowed to be unbounded. Assuming certain integrability conditions on $ \lambda $ and $ \lambda^{-1} $ depending on $ p $ and the dimension, we show local boundedness. Moreover, we provide counterexamples to regularity showing that the integrability conditions are optimal for every $ p > 1 $.

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退化系数的$p$-Laplacian算子的局部有界性

研究了一类原型为$ \nabla \cdot (\lambda |\nabla u|^{p-2}\nabla u) = 0 $的非线性非一致椭圆型方程的子解的局部有界性，其中变系数$ 0\leq\lambda $及其逆系数$ \lambda^{-1} $允许无界。根据$ p $和维数的不同，在$ \lambda $和$ \lambda^{-1} $上假设一定的可积条件，给出了局部有界性。此外，我们还提供了正则性的反例，证明了每$ p > 1 $的可积性条件都是最优的。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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