Global Gradient Estimates of Very Weak Solutions for a General Class of Quasilinear Elliptic Equations

被引：0
作者：
Sun-Sig Byun
Minkyu Lim
机构：
[1] Seoul National University,Department of Mathematical Sciences and Research Institute of Mathematics
[2] Seoul National University,Research Institute of Mathematics
来源：
The Journal of Geometric Analysis | 2023年 / 33卷
关键词：
Very weak solution; -Laplace equation; Gradient estimates; Higher integrability; A priori estimate; Lipschitz truncation; Primary 35B65; Secondary 35J70;
D O I：
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学科分类号：
摘要：
We are concerned with global gradient estimates of very weak solutions for a general class of quasilinear elliptic equations with nonstandard growth. We establish such estimates under basic structure assumptions on the nonlinearity and natural geometric assumption on the complement of the bounded domain. Our approach is based on a generalized Lipschitz truncation alongside a generalized self-improving property of thick sets. This work provides a careful analysis of the thickness described in Adimurthi and Phuc (Calc Var Partial Differ Equ 54:3107–3139, 2015), Harjulehto and Hästö (Z Anal Anwend 38(1):73–96, 2019), Heinonen et al (Potential theory of degenerate elliptic equations, Oxford University Press, Oxford, 1993).
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