Séminaire Modélisation, Optimisation, Dynamique

Existence and regularity of solutions to nonlinear elliptic equations without sign condition

par M. Jaouad Igbida (Université d'El Jadida, Maroc)

Europe/Paris
203 (XLIM)

203

XLIM

FST-Université de Limoges, 123, Av. Albert Thomas.
Description
In this talk we study the existence of bounded weak solutions for some nonlinear Dirichlet problems in a bounded domains. Without any sign condition on the term which growth quadratically on the gradient and for a given function f in $L^m(\Omega)$ with $m > N/2,$ we prove the existence of bounded weak solutions via $L^1$-estimates. Our methods relay on Schauder fixed point theorem, a priori estimates and Stampacchia’s $L^1$-regularity.