Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space

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.

Author Details

Youssef Akdim

Chakir Allalou

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