#### 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

$L\left(u\right)={\int }_{\partial \Omega }\phantom{\rule{0.3em}{0ex}}u\phantom{\rule{0.3em}{0ex}}d\sigma -{\int }_{\Omega }u\phantom{\rule{0.3em}{0ex}}dx$

in the class of convex functions $u$ with prescribed determinant $det{D}^{2}u=f$.

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
Primary: 35J96
Secondary: 35J66