Concavity principles for nonautonomous elliptic equations and applications

TL;DR

This paper develops new concavity results for positive solutions of anisotropic semilinear elliptic equations with spatially varying coefficients, extending classical concavity principles to more complex, nonautonomous cases.

Contribution

It introduces novel methods to establish almost concavity for solutions to elliptic equations with space-dependent diffusion and source terms, broadening the scope of existing concavity principles.

Findings

Established almost concavity for solutions with spatially dependent coefficients

Extended classical concavity results to anisotropic, nonautonomous elliptic problems

Provided new analytical tools for studying solution properties in complex PDEs

Abstract

In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming to get almost concavity results for a relevant class of anisotropic semilinear elliptic problems with spatially dependent source and diffusion.