The Monge-Ampère Equation with Guillemin Boundary Conditions

Abstract

Existence and boundary regularity away from the corners are established for two-dimensional Monge-Ampère equations on convex polytopes with Guillemin boundary conditions. An important step is to derive an expansion in terms of functions $y^n$ and $y^n\log y$ for solutions to equations of the form $\det D^{2}u(x,y)=y^{-1}$ in a half-ball.

arXiv comment19 pages