Methods and Applications of Analysis

Volume 24 (2017)

Number 4

Partial regularity of solutions to the second boundary value problem for generated Jacobian equations

Pages: 445 – 476

DOI: https://dx.doi.org/10.4310/MAA.2017.v24.n4.a2

Author

Yash Jhaveri (Department of Mathematics, ETH Zürich, Switzerland)

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.

Keywords

generated Jacobian equations, Monge–Ampère-type equations, partial regularity

2010 Mathematics Subject Classification

35J96

Full Text (PDF format)

Supported in part by the ERC grant “Regularity and Stability in Partial Differential Equations (RSPDE)”.

Received 30 September 2016

Accepted 21 March 2018

Published 20 April 2018