A Compactness Condition for the Theorem of Sums in a Class of Non-Uniformly Elliptic PDEs

Abstract

In the theory of viscosity solutions for second-order, degenerate elliptic PDEs, the Ishii-Lions method is a commonly used strategy, and the theorem of sums is the main analytical tool. As noted by Porretta and Priola, uniformly elliptic PDEs admit a version of the theorem of sums without the squared term due to a compactness argument. Here, we introduce a larger class of PDEs for which the compactness argument holds.