Global gradient estimates for nonlinear equations of p-Laplace type from composite materials

Yunsoo Jang; Youchan Kim

doi:10.1016/j.jmaa.2018.10.023

Global gradient estimates for nonlinear equations of p-Laplace type from composite materials

Yunsoo Jang, Youchan Kim

Department of Mathematics

Yonsei University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study global gradient estimates for the weak solution to divergence form nonlinear elliptic equations with p-growth nonlinearities from composite materials. We assume that the domain is bounded and is composed of disjoint Reifenberg flat domains and the nonlinearities have small BMO seminorms in each subdomain. Under these assumptions, based on our new geometric observation for disjoint Reifenberg domains and gradient estimates for nonlinear equations with measurable p-growth nonlinearities, we establish global W^1,q estimates for p≤q<∞.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	471
Issue number	1-2
DOIs	https://doi.org/10.1016/j.jmaa.2018.10.023
State	Published - Mar 2019

Keywords

Composite material
Measurable nonlinearity
Nonlinear elliptic equations
Reifenberg domain
p-growth condition

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10.1016/j.jmaa.2018.10.023

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abstract = "We study global gradient estimates for the weak solution to divergence form nonlinear elliptic equations with p-growth nonlinearities from composite materials. We assume that the domain is bounded and is composed of disjoint Reifenberg flat domains and the nonlinearities have small BMO seminorms in each subdomain. Under these assumptions, based on our new geometric observation for disjoint Reifenberg domains and gradient estimates for nonlinear equations with measurable p-growth nonlinearities, we establish global W1,q estimates for p≤q<∞.",

keywords = "Composite material, Measurable nonlinearity, Nonlinear elliptic equations, Reifenberg domain, p-growth condition",

author = "Yunsoo Jang and Youchan Kim",

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AB - We study global gradient estimates for the weak solution to divergence form nonlinear elliptic equations with p-growth nonlinearities from composite materials. We assume that the domain is bounded and is composed of disjoint Reifenberg flat domains and the nonlinearities have small BMO seminorms in each subdomain. Under these assumptions, based on our new geometric observation for disjoint Reifenberg domains and gradient estimates for nonlinear equations with measurable p-growth nonlinearities, we establish global W1,q estimates for p≤q<∞.

KW - Composite material

KW - Measurable nonlinearity

KW - Nonlinear elliptic equations

KW - Reifenberg domain

KW - p-growth condition

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Global gradient estimates for nonlinear equations of p-Laplace type from composite materials

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