Concave power solutions of the Dominative p-Laplace equation

2019/01/21 by Høeg, Fredrik Arbo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.07053

Abstract

In this paper, we study properties of solutions of the Dominative p-Laplace equation with homogeneous Dirichlet boundary conditions in a bounded convex domain Ω. For the equation -D_p u= 1, we show that √(u) is concave, and for the eigenvalue problem D_p u + λu=0, we show that log u is concave.

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