Global gradient estimates for the borderline case of double phase problems with BMO coefficients in nonsmooth domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Byun, Sun-Sig^1,2  Oh, Jehan¹ 

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

关键词: BMO coefficient;    Calderon-Zygmund estimate;    Double phase problem;    Non-uniformly elliptic equation;    Reifenberg flat domain;   

DOI  :  10.1016/j.jde.2017.03.025

来源: Elsevier

【 摘 要 】

We consider a double phase problem with BMO coefficient in divergence form on a bounded nonsmooth domain. The problem under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm according to the position, which describes a feature of strongly anisotropic materials. We obtain the global Calderon-Zygmund type estimates for the distributional solution in the case that the associated nonlinearity has a small BMO and the boundary of the domain is sufficiently flat in the Reifenberg sense. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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