Some qualitative properties of solutions of quasilinear elliptic equations and applications

Abstract

We study quasilinear elliptic equations of Leray-Lions type in W1, p(Ω), maximum principles, nonexistence and existence of solutions, the control of lower (upper) bound for essential supremum (essential infimum) of solutions, sign-changing solutions, local and global oscillation of solutions, geometry of domain, generating singularities of solutions, and lower bounds on constants appearing in Schauder, Agmon, Douglis, and Nirenberg estimates. © 2001 Academic Press.