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

Nam Le; Ovidiu Savin

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arXiv · 1109.5676

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

Nam Le·Ovidiu Savin

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Abstract

We consider minimizers of linear functionals of the type $$L(u)=\int_{\p Ω} u \, d σ- \int_Ω u \, dx$$ 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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Nam Le, Ovidiu Savin. 2011-09-26. Some minimization problems in the class of convex functions with prescribed determinant. https://arxiv.org/abs/1109.5676

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