ON THE REGULARITY OF SOLUTIONS TO MONGE-AMPÈRE EQUATIONS ON HESSIAN MANIFOLDS

DOI10.1081/PDE-100107825zbMath0990.35029OpenAlexW2000167822MaRDI QIDQ2777585

Jeff A. Viaclovsky, Luis A. Caffarelli

Publication date: 21 August 2002

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-100107825

zbMATH Keywords

\(C^{2,\alpha}\) regularity of locally convex viscosity solutionsPogorelov-type counterexamples

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45)

Related Items (8)

Entire invariant solutions to Monge-Ampère equations ⋮ Monge-Ampère Equation with Bounded Periodic Data ⋮ Convergence of the Hesse-Koszul flow on compact Hessian manifolds ⋮ A Liouville theorem for solutions of the Monge--Ampère equation with periodic data. ⋮ Convergence rates for discretized Monge-Ampère equations and quantitative stability of optimal transport ⋮ Permanental Point Processes on Real Tori, Theta Functions and Monge–Ampère Equations ⋮ Implications of energy conditions on standard static space-times ⋮ An optimal transport approach to Monge-Ampère equations on compact Hessian manifolds

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