Coupling Levy measures and comparison principles for viscosity solutions
arXiv:1805.06955
Abstract
We prove new comparison principles for viscosity solutions of non-linear integro-differential equations. The operators to which the method applies include but are not limited to those of Lévy-Itô type. The main idea is to use an optimal transport map to couple two different Lévy measures, and use the resulting coupling in a doubling of variables argument
39 pages, no figures, added a new section discussing several examples and clarified and corrected some of the proofs related to the background material in the appendix, to appear in Transactions of the American Mathematical Society