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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

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 for the...

A Superconvergence result for mixed finite element approximations of the eigenvalue problem

Qun Lin, Hehu Xie (2012)

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

In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...

A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗

Qun Lin, Hehu Xie (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...

A symmetrization result for nonlinear elliptic equations.

Vincenzo Ferone, Basilio Messano (2004)

Revista Matemática Complutense

We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W01,p (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.

A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces

Akihito Unai (2018)

Applications of Mathematics

We shall prove a weak comparison principle for quasilinear elliptic operators - div ( a ( x , ∇ u ) ) that includes the negative p -Laplace operator, where a : Ω × ℝ N → ℝ N satisfies certain conditions frequently seen in the research of quasilinear elliptic operators. In our result, it is characteristic that functions which are compared belong to different spaces.

Currently displaying 101 – 120 of 1236