TY - JOUR
T1 - Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space
AU - Akdim , Youssef
AU - Allalou , Chakir
JO - Journal of Mathematical Study
VL - 4
SP - 375
EP - 397
PY - 2015
DA - 2015/12
SN - 48
DO - http://doi.org/10.4208/jms.v48n4.15.05
UR - https://global-sci.org/intro/article_detail/jms/9943.html
KW - Weighted variable exponent Sobolev spaces, truncations, Young's Inequality, elliptic operators.
AB - <p style="text-align: justify;">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 $Ω$&nbsp; 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.</p>