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2013 Some minimization problems in the class of convex functions with prescribed determinant
Nam Le, Ovidiu Savin
Anal. PDE 6(5): 1025-1050 (2013). DOI: 10.2140/apde.2013.6.1025

Abstract

We consider minimizers of linear functionals of the type

L ( u ) = Ω u d σ Ω u d x

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.

Citation

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Nam Le. Ovidiu Savin. "Some minimization problems in the class of convex functions with prescribed determinant." Anal. PDE 6 (5) 1025 - 1050, 2013. https://doi.org/10.2140/apde.2013.6.1025

Information

Received: 5 April 2012; Revised: 12 December 2012; Accepted: 28 February 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1280.49057
MathSciNet: MR3125549
Digital Object Identifier: 10.2140/apde.2013.6.1025

Subjects:
Primary: 35J96
Secondary: 35J66

Rights: Copyright © 2013 Mathematical Sciences Publishers

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