$L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms

$L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms

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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