Open AccessGradient estimates for the strong $p(x)$-Laplace equation
Author(s) -
Chao Zhang,
Xia Zhang,
Shulin Zhou
Publication year - 2017
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2017175
Subject(s) - mathematics , mathematical analysis , laplace transform , laplace's equation , green's function for the three variable laplace equation , physics , mathematical physics , partial differential equation
We study nonlinear elliptic equations of strong $p(x)$-Laplacian type to obtain an interior Calderon-Zygmund type estimates by finding a correct regularity assumption on the variable exponent $p(x)$. Our proof is based on the maximal function technique and the appropriate localization method.
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