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 - <p style="text-align: justify;">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 $W^{-1,q}(\Omega)$.</p>