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

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.

References in corpus (2)

• Interior estimates for solutions of Abreu's equation
• $W^{2,1}$ regularity for solutions of the Monge-Ampère equation

Cited by in corpus (2)

• Boundary regularity for solutions to the linearized Monge-Ampère equations
• Interior second derivative estimates for solutions to the linearized Monge--Ampère equation