Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems  

作　　者：Youssef Akdim Chakir Allalou 

机构地区：[1]Facult Poly-disciplinaire de Taza,B.P 1223 Taza Gare, Maroc

出　　处：《Analysis in Theory and Applications》2014年第3期318-343,共26页分析理论与应用（英文刊）

摘　　要：In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β（u）-div（α（x, Du）＋F（u）） ∈ f in fΩ, where f ∈ L1 （Ω）. A vector field a（.,.） is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β（u）-div（α（x, Du）＋F（u）） ∈ f in fΩ, where f ∈ L1 （Ω）. A vector field a（.,.） is a Carath6odory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.

关 键 词：Weighted Sobolev spaces Hardy inequality TRUNCATIONS maximal monotone graphe degenerated elliptic operators. 

分 类 号：O175[理学—数学]