Singular Solutions to the Monge-Ampere Equation
By: Connor R. Mooney
Publisher: [publisher not identified]
Published: 2015
Place of publication: [New York, N.Y.?]
Language: eng
Description: 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.
Notes: Department: Mathematics.

Thesis advisor: Ovidiu Savin.

Thesis (Ph.D.)--Columbia University, 2015.