Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems (Analysis in Theory and Applications, 2014)
In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) i f$ in $Ω $, where $f\in L^{1}(Ω )$. A vector field $a(·,·)$ 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.
Keywords: Weighted Sobolev spaces; Hardy inequality; Truncations; maximal monotone graph; degenerated elliptic operators.