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Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems
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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.
作者 Youssef Akdim Chakir Allalou
机构地区 Facult Poly-disciplinaire de Taza
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）
关键词 Weighted Sobolev spaces Hardy inequality TRUNCATIONS maximal monotone graphe degenerated elliptic operators. Weighted Sobolev spaces, Hardy inequality, Truncations, maximal monotone graphe,degenerated elliptic operators.
分类号 O175 [理学—基础数学]
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参考文献18

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Analysis in Theory and Applications
2014年 第3期

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