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

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

2011-09-26

arxiv.org/abs/1109.5676v1

Mathematics

Analysis of PDEs

Scientific paper

We consider minimizers of linear functionals of the type $$L(u)=\int_{\p
\Omega} u \, d \sigma - \int_{\Omega} u \, dx$$ 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.

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