Academic Commons

Theses Doctoral

Singular Solutions to the Monge-Ampere Equation

Mooney, Connor R.

This thesis contains the author's results on singular solutions to the Monge-Ampere equation \det D^2u = 1. We first prove that solutions are smooth away from a small closed singular set of Hausdorff (n-1)-dimensional measure zero. We also construct solutions with a singular set of Hausdorff dimension n-1, showing that this result is optimal. As a consequence we obtain unique continuation for the Monge-Ampere equation. Finally, we prove an interior W^{2,1} estimate for singular solutions, and we construct an example to show that this estimate is optimal.



  • thumnail for Mooney_columbia_0054D_12572.pdf Mooney_columbia_0054D_12572.pdf binary/octet-stream 919 KB Download File

More About This Work

Academic Units
Thesis Advisors
Savin, Ovidiu
Ph.D., Columbia University
Published Here
April 10, 2015
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.