The Monge-Ampère Equation with Guillemin Boundary Conditions (1401.3767v1)

Published 15 Jan 2014 in math.AP and math.DG

Abstract: Existence and boundary regularity away from the corners are established for two-dimensional Monge-Amp`{e}re 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 $\det D^2u(x,y) = y^{-1}$ in a half-ball.

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Authors (1)

Daniel Rubin

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