Displaying similar documents to “An L 1 -theory of existence and uniqueness of solutions of nonlinear elliptic equations”

A strongly degenerate quasilinear equation : the elliptic case

Fuensanta Andreu, Vicent Caselles, José Mazón (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation u - div 𝐚 ( u , D u ) = v , where v L 1 , 𝐚 ( z , ξ ) = ξ f ( z , ξ ) , and f is a convex function of ξ with linear growth as ξ , satisfying other additional assumptions. In particular, this class includes the case where f ( z , ξ ) = ϕ ( z ) ψ ( ξ ) , ϕ > 0 , ψ being a convex function with linear growth as ξ . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions...

Regularity for entropy solutions of parabolic p-Laplacian type equations.

Sergio Segura de León, José Toledo (1999)

Publicacions Matemàtiques

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In this note we give some summability results for entropy solutions of the nonlinear parabolic equation u - div a (x, ∇u) = f in ] 0,T [xΩ with initial datum in L(Ω) and assuming Dirichlet's boundary condition, where a(.,.) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L (]0,T[xΩ) and Ω is a domain in R. We find spaces of type L(0,T;M(Ω)) containing the entropy solution and its gradient. We also include some summability results when f = 0 and the p-Laplacian...

Obstacle problems for scalar conservation laws

Laurent Levi (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in L . Lastly, we study the behaviour of this solution and its stability properties...