$L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms
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@Article{ATA-33-46,
author = {Y. Akdim, M. Belayachi and M. El Moumni},
title = {$L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms},
journal = {Analysis in Theory and Applications},
year = {2017},
volume = {33},
number = {1},
pages = {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 $W^{-1,q}(\Omega)$.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n1.5}, url = {http://global-sci.org/intro/article_detail/ata/4615.html} }
TY - JOUR
T1 - $L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms
AU - Y. Akdim, M. Belayachi & M. El Moumni
JO - Analysis in Theory and Applications
VL - 1
SP - 46
EP - 58
PY - 2017
DA - 2017/01
SN - 33
DO - http://doi.org/10.4208/ata.2017.v33.n1.5
UR - https://global-sci.org/intro/article_detail/ata/4615.html
KW - $L^\infty$-estimate, nonlinear elliptic equations, rearrangement, Sobolev spaces.
AB -
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 $W^{-1,q}(\Omega)$.
Y. Akdim, M. Belayachi and M. El Moumni. (2017). $L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms.
Analysis in Theory and Applications. 33 (1).
46-58.
doi:10.4208/ata.2017.v33.n1.5
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