Partial Regularity of Solutions to the Second Boundary Value Problem for Generated Jacobian Equations

Abstract

We prove that outside of a closed singular set of measure zero solutions to the second boundary value problem for generated Jacobian equations are smooth.

arXiv commentThis version corrects an error in the published manuscript. The generating function must be $C^{2,\alpha }$ to begin with, not $C^2$. Corresponding changes made throughout