The AE Theorem and addition theorems for quasi-convex functions

Abstract

The main point of this paper is to prove the following useful result: If the almost everywhere 2-jet of a locally quasi-convex function u satisfies a degenerate elliptic constraint F, then u is F-subharmonic, i.e., u is a viscosity F-subsolution. This AE Theorem makes otherwise difficult results transparent. Some instances of this are presented, including two versions of addition, and a comparison theorem.

The relationship of the Addition Theorem to comparison for gradient-free constant coefficient equations is discussed in a new section

Cited by in corpus (4)

• Notes on the differentiation of quasi-convex functions
• Comparison principles by monotonicity and duality for constant coefficient nonlinear potential theory and PDEs
• Characterizing the Strong Maximum Principle
• Comparison principles for nonlinear potential theories and PDEs with fiberegularity and sufficient monotonicity