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

TL;DR

This paper proves that solutions to the second boundary value problem for generated Jacobian equations are smooth outside a measure-zero singular set, advancing understanding of their regularity properties.

Contribution

It establishes partial regularity results for solutions to a class of generated Jacobian equations, showing smoothness outside a negligible singular set.

Findings

Solutions are smooth outside a measure-zero singular set.

The singular set where solutions may not be smooth has measure zero.

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.