Maximum principles for viscosity solutions of weakly elliptic equations

Abstract

Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions. Here we consider degenerate elliptic equations, where the main term is a partial trace of the Hessian matrix of the solution. We establish maximum principles in domains that are unbounded in some directions, contained in slabs, and extended maximum principles, which lead to removable singularity results.

Keywords

• weighted partial trace operators
• fully nonlinear elliptic equations
• viscosity solutions
• holder estimates