Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space
Year: 2015
Author: Youssef Akdim, Chakir Allalou
Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 375–397
Abstract
In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$ where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n4.15.05
Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 375–397
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Weighted variable exponent Sobolev spaces truncations Young's Inequality elliptic operators.