Gradient estimates for the strong $p(x)$-Laplace equation

Chao Zhang; Xia Zhang; Shulin Zhou

doi:10.3934/dcds.2017175

Article Contents

2017, Volume 37, Issue 7: 4109-4129. Doi: 10.3934/dcds.2017175

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Gradient estimates for the strong $p(x)$-Laplace equation

1.
Department of Mathematics, Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
3.
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

* Corresponding author
* Corresponding author

Received: May 31, 2016

Revised: January 31, 2017

Published: August 2017

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Abstract

We study nonlinear elliptic equations of strong $p(x)$-Laplacian type to obtain an interior Calderón-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.

Keywords:

Nonlinear Calderón-Zygmund theory,
strong $p(x)$-Laplacian,
variable exponents,
generalized Lebesgue and Sobolev spaces.

Mathematics Subject Classification: Primary: 35R05, 35J92; Secondary: 35J15, 35J25.

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References

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