Some Qualitative Properties of Solutions of Quasilinear Elliptic Equations and Applications

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.