2022 •
Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations
Authors:
Niklas L.P. Lundström, Marcus Olofsson, Olli Toivanen
Abstract:AbstractWe give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear nonhomogeneous degenerate elliptic equations on the form $$ F(x,u,Du,D^{2}u) = 0 $$F(x,u,Du,AbstractWe give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear nonhomogeneous degenerate elliptic equations on the form $$ F(x,u,Du,D^{2}u) = 0 $$F(x,u,Du,D2u)=0 under suitable assumptions allowing for non-Lipschitz growth in the gradient term. In case of smooth boundaries, we also prove a Hopf lemma, a 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, e.g., to weak solutions of an eigenvalue problem for the variable exponent p-Laplacian.(Read More)
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