Some minimum principles for a class of nonlinear elliptic problems in divergence form

Abstract

In this paper we study a general class of nonlinear elliptic problems in divergence form. First, for a natural subclass of coefficients, we prove that a suitable transformation of the solution is strictly concave when the given domain is strictly convex. Then, making use of this convexity property, these new minimum principles are applied to find a priori estimates for the solutions, in terms of the mean curvature of the boundary of the underlying domain.