Pseudo-monotonicity and degenerate elliptic operators of second order.
Leray Lions degenerated problem with general growth condition.
On the solvability of degenerated quasilinear elliptic problems.
Solvability of degenerated parabolic equations without sign condition and three unbounded nonlinearities.
Higher order nonlinear degenerate elliptic problems with weak monotonicity.
Strongly nonlinear degenerated elliptic unilateral problems via convergence of truncations.
Musielak−Orlicz−Sobolev spaces on arbitrary metrique space
In this article we define Musielak−Orlicz−Sobolev spaces on arbitrary metric spaces with finite diameter and equipped with finite, positive Borel regular outer measure. We employ a Hajlasz definition, which uses a pointwise maximal inequality. We prove that these spaces are Banach, that the Poincaré inequality holds, and that the Lipschitz functions are dense. We develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. As an application,...
Existence of a renormalized solution of nonlinear degenerate elliptic problems
We study a general class of nonlinear elliptic problems associated with the differential inclusion in Ω where . The vector field a(·,·) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general -data.
Existence of solutions of degenerated unilateral problems with data
In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type where is a Leray-Lions operator and is a Carathéodory function having natural growth with respect to and satisfying the sign condition. The second term is such that, and .
Existence results for quasilinear degenerated equations via strong convergence of truncations.
In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x,u,∇u) = f, where A is a Leray-Lions operator from W (Ω,ω) into its dual, while g(x,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong either to W(Ω,ω*) or to L(Ω).
Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems
An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form , where is a Leray-Lions operator from into its dual, while is a nonlinear term which has a growth condition with respect to and no growth with respect to , but it satisfies a sign condition on , the second term belongs to .
Page 1