$L^∞$-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms (Analysis in Theory and Applications, 2017)
In this work, we will prove the existence of bounded solutions in $W_{0}^{1,p}(Ω) \cap L^{∞}(Ω)$ for nonlinear elliptic equations $- div(a(x,u, abla u)) + g(x,u, abla u) + H(x, abla u) = f$, where $a$, $g$ and $H$ are Carathéodory functions which satisfy some conditions, and the right hand side $f$ belongs to $W^{-1,q}(Ω)$.
Keywords: $L^∞$-estimate; nonlinear elliptic equations; rearrangement; Sobolev spaces.