The Monge-Ampère Equation with Guillemin Boundary Conditions

2014/01/15 by Daniel Rubin, Rubin, Daniel
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1401.3767

19 pages

arxiv created 2014/01/15 · arxiv updated 2014/01/17

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 yⁿ and yⁿlog y for solutions to equations of the form det D²u(x,y) = y^-1 in a half-ball.

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