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Local Hölder estimates for non-uniformly variable exponent elliptic equations in divergence form

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  18 December 2017

Fengping Yao
Fengping Yao*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China ([email protected])
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Abstract

In this paper we obtain the local Hölder regularity of the gradients of weak solutions for a class of non-uniformly nonlinear variable exponent elliptic equations in divergence form

including the following special model

under some proper assumptions on Ai and the Hölder continuous functions f, pi(x) for i = 1, 2.

Keywords

C1,αgradientdivergencenon-uniformlyvariable exponentelliptic

MSC classification

Secondary: 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 1 , February 2018 , pp. 211 - 224
Copyright
Copyright © Royal Society of Edinburgh 2018 

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