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

Cristian Enache; Rafael Lopez

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arXiv · 2603.12931

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

Cristian Enache·Rafael Lopez

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Abstract

In this paper we study a general class of nonlinear elliptic problems in divergence form. First, we prove that the solutions to these problems satisfy a convexity property when the given domain is strictly convex. Then, making use of this convexity property, we develop some minimum principles for an appropriate $P$-function, in the sense of L.~E.~Payne. Finally, this new minimum principle is applied to find a priori estimates for the solutions, in terms of the mean curvature of the boundary of the underlying domain.

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Cristian Enache, Rafael Lopez. 2026-03-13. Some minimum principles for a class of nonlinear elliptic problems in divergence form. https://arxiv.org/abs/2603.12931

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