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Volume 33, Issue 1
$L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms

Y. Akdim, M. Belayachi & M. El Moumni

Anal. Theory Appl., 33 (2017), pp. 46-58.

Published online: 2017-01

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  • 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 $W^{-1,q}(\Omega)$.

  • AMS Subject Headings

35J60, 46E30, 46E35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-33-46, author = {}, 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 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 & M. El Moumni. (1970). $L^∞$-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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