Strong MTW type condition to local Holder regularity in generated Jacobian equations

Abstract: n this talk, we present a proof of local Holder regularity of solutions to generated Jacobian equations as a generalization of optimal transport case, which is proved by George Loeper. We compare structures of generated Jacobian equations with optimal transport, and point out differences with difficulties which the differences can cause. For local Holder regularity theory, we use (G3s) condition and solution in Alexandrov sense. (G3s) is a strict positiveness type condition on MTW tensor associated to the generating function G, and Alexandrov solution is a solution that satisfies pullback measure condition. (G3s) is used to show a quantitative version of (glp), which gives some room for G-subdifferentials of solutions. Then the inequality for Holder regularity is shown by comparing volumes of G-subdifferentials using the fact that our solutions is in Alexandrov sense.

mathematical physicsanalysis of PDEs

Audience: researchers in the topic

TAMU: Mathematical Physics and Harmonic Analysis Seminar