@Article{ATA-30-318, author = {}, title = {Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {3}, pages = {318--343}, abstract = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.8}, url = {http://global-sci.org/intro/article_detail/ata/4496.html} }