The AE Theorem and addition theorems for quasi-convex functions
Analysis of PDEs
2016-08-02 v3 Complex Variables
Differential Geometry
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.
Keywords
Cite
@article{arxiv.1309.1770,
title = {The AE Theorem and addition theorems for quasi-convex functions},
author = {F. Reese Harvey and H. Blaine Lawson},
journal= {arXiv preprint arXiv:1309.1770},
year = {2016}
}
Comments
The relationship of the Addition Theorem to comparison for gradient-free constant coefficient equations is discussed in a new section