TY - JOUR
T1 - Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems
AU - Y. Akdim & C. Allalou
JO - Analysis in Theory and Applications
VL - 3
SP - 318
EP - 343
PY - 2014
DA - 2014/10
SN - 30
DO - http://doi.org/10.4208/ata.2014.v30.n3.8
UR - https://global-sci.org/intro/article_detail/ata/4496.html
KW - Weighted Sobolev spaces, Hardy inequality, Truncations, maximal monotone graph, degenerated elliptic operators.
AB - <p style="text-align: justify;">In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $\beta(u)-div(a(x,Du)+F(u))\ni f$ in $\Omega $, where $f\in L^{1}(\Omega )$. A vector field $a(\cdot,\cdot)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general $L^1$-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.</p>