Year: 2017
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 46–58
Abstract
In this work, we will prove the existence of bounded solutions in $W_{0}^{1,p}(\Omega) \cap L^{\infty}(\Omega)$ for nonlinear elliptic equations $-\mbox{ div}(a(x,u,\nabla u)) + g(x,u,\nabla u) + H(x,\nabla u) = f$, where $a$, $g$ and $H$ are Carathéodory functions which satisfy some conditions, and the right hand side $f$ belongs to $W^{-1,q}(\Omega)$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2017.v33.n1.5
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 46–58
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: $L^\infty$-estimate nonlinear elliptic equations rearrangement Sobolev spaces.
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