Existence And Regularity Of Solutions To Nonlinear Elliptic Equations Without Sign Condition

Jaouad IGBIDA, Ahmed JAMEA and

Abstract

In this paper 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(Ω) with m > N/2, we prove the existence of bounded weak solutions via L∞-estimates. Our methods relay on Schauder fixed point theorem, a priori estimates and Stampacchia’s L∞-regularity.