Détails Publication
WEAK SOLUTIONS FOR ANISOTROPIC NONLINEAR ELLIPTIC PROBLEM WITH VARIABLE EXPONENT AND MEASURE DATA,
Auteur(s): Blaise Kone , Stanislas Ouaro and Safimba Soma
Auteur(s) tagués:
KONE Blaise ;
OUARO Stanislas ;
SOMA Safimba
Renseignée par : KONE Blaise
Résumé
We study in this paper the anisotropic nonlinear boundary value problem
N ∂ ∂u
− ∑∂x ai x,∂x =μ in Ω, u=0 on ∂Ω, where Ω is a smooth bounded open
i=1i i
domain in RN , N ≥ 3 and μ a bounded Radon measure. We prove the existence of a weak energy solution for this anisotropic nonlinear elliptic problem with different vari- able exponents, so that, the functional setting involves anisotropic variable exponent Sobolev spaces and Marcinkiewicz spaces.
Mots-clés
Generalized Lebesgue-Sobolev spaces, anisotropic Sobolev spaces, weak solution, bounded Radon measure, electrorheological fluids, Marcinkiewicz spaces