L∞-Estimates for Nonlinear Degenerate Elliptic Problems with p-growth in the Gradient
Youssef Akdim, Mohammed Belayachi · Advances in Science Technology and Engineering Systems Journal · 2017
In this work, we will prove the existence of bounded solutions for the nonlinear elliptic equations div(a(x, u, ∇u)) = g(x, u, ∇u)divf , in the setting of the weighted Sobolev space W 1,p (Ω, w) where a, g are Carathéodory functions which satisfy some conditions and f satisfies suitable summability assumption.