RESEARCH ARTICLE

Regularity for anisotropic solutions to some nonlinear elliptic system

  • Hongya GAO ,
  • Shuang LIANG ,
  • Yi CUI
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  • College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received date: 20 Nov 2014

Accepted date: 29 Dec 2014

Published date: 02 Dec 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

This paper deals with anisotropic solutions uW1,(pi)(Ω,N) to the nonlinear elliptic system

Σi=1nDi(aiα(χ,Du(χ)))=Σi=1nDiFiα(χ), α=1,2,...,N,

We present a monotonicity inequality for the matrix a=(aiα)N×n,whichguarantees global pointwise bounds for anisotropic solutionsu.

Cite this article

Hongya GAO , Shuang LIANG , Yi CUI . Regularity for anisotropic solutions to some nonlinear elliptic system[J]. Frontiers of Mathematics in China, 2016 , 11(1) : 77 -87 . DOI: 10.1007/s11464-015-0443-5

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