Détails Publication
Weak and entropy solutions to nonlinear Neumann boundary-value problems with variable exponents,
Auteur(s): Stanislas Ouaro and Safimba Soma
Auteur(s) tagués:
SOMA Safimba ;
OUARO Stanislas
Renseignée par : SOMA Safimba
Résumé
In this article, we study the following nonlinear Neumann boundary-value problem diva(x,ru)þjujp(x)2 u1⁄4f in , @u 1⁄4 0 on @, where is a
@
smooth bounded open domain in RN, N 3, @u is the outer unit normal @
derivative on @, div a(x, ru) a p(x)-Laplace type operator. We prove the existence and uniqueness of a weak solution for f 2 L( p)0 (), the existence and uniqueness of an entropy solution for L1-data f independent of u and the existence of weak solutions for f dependent on u. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.
Mots-clés
generalized Lebesgue and Sobolev spaces, weak solution, entropy solution, p(x)-Laplace operator