Wolff potentials and measure data vectorial problems with Orlicz growth

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

On Elliptic Equations in Orlicz Spaces Involving Natural Growth Term and Measure Data

and Applied Analysis 3 2. Preliminaries LetM : R → R be anN-function, that is,M is continuous, convex, withM t > 0 for t > 0, M t /t → 0 as t → 0 and M t /t → ∞ as t → ∞. The N-function M conjugate to M is defined byM t sup{st −M s : s > 0}. Let P and Q be two N-functions. P Q means that P grows essentially less rapidly than Q; that is, for each ε > 0, P t Q εt −→ 0 as t −→ ∞. 2.1 The N-functio...

Elliptic Unilateral Problems in Orlicz Space and L 1 Data

In this paper, we shall be concerned with the existence result of Unilateral problem associated to the equations of the form, Au+ g(x, u,∇u) = f, where A is a Leray-Lions operator from its domain D(A) ⊂ W 1 0 LM (Ω) into WEM (Ω). On the nonlinear lower order term g(x, u,∇u), we assume that it is a Carathéodory function having natural growth with respect to |∇u|, and satisfies the sign condition...

Semicontinuity of Vectorial Functionals in Orlicz-sobolev Spaces

We study integral vectorial functionals F(u;) ? Z f(x; u(x); Du(x))dx where f satisses quasi-convexity assumption and its growth is controlled in term of N-functions. We obtain semicontinuity results in the weak * topology of Orlicz-Sobolev spaces.

Non convex technologies and economic efficiency measure with imprecise data