Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations

2020/05/07 by Lundström, Niklas L. P., Olofsson, Marcus, Toivanen, Olli · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.03338

Abstract

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form F(x,u,Du,D²u) = 0 under suitable structure conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply to weak solutions of an eigenvalue problem for the variable exponent p-Laplacian.

Cited by

• Estimates for viscosity solutions of fully nonlinear equations near smooth boundaries

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