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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:471

Article

Jang, Yunsoo¹  Kim, Youchan² 

[1] Yonsei Univ, CMAC, Seoul 03722, South Korea

[2] Univ Seoul, Dept Math, Seoul 02504, South Korea

关键词: Nonlinear elliptic equations;    p-growth condition;    Measurable nonlinearity;    Composite material;    Reifenberg domain;   

DOI  :  10.1016/j.jmaa.2018.10.023

来源: Elsevier

【 摘 要 】

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,W-q estimates for p <= q < infinity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free