Vol. 6, No. 5, 2013

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Some minimization problems in the class of convex functions with prescribed determinant

Nam Q. Le and Ovidiu Savin

Vol. 6 (2013), No. 5, 1025–1050
Abstract

We consider minimizers of linear functionals of the type

L(u) =Ωudσ Ωudx

in the class of convex functions u with prescribed determinant detD2u = f.

We obtain compactness properties for such minimizers and discuss their regularity in two dimensions.

Keywords
boundary regularity, convex minimizer, fourth-order elliptic equation, prescribed determinant
Mathematical Subject Classification 2010
Primary: 35J96
Secondary: 35J66
Milestones
Received: 5 April 2012
Revised: 12 December 2012
Accepted: 28 February 2013
Published: 3 November 2013
Authors
Nam Q. Le
Department of Mathematics
Columbia University
New York, NY 10027
United States
Ovidiu Savin
Department of Mathematics
Columbia University
New York, NY 10027
United States