A note on interior $$W^{2,1+ \varepsilon }$$estimates for the Monge–Ampère equation

By Guido De Philippis, Alessio Figalli, O. Savin. 2012

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By a variant of the techniques introduced by the first two authors in De Philippis and Figalli (Invent Math 2012) to prove that second derivatives of solutions to the Monge–Ampère equation are locally in $$L\log L$$, we obtain interior $$W^{2,1+\varepsilon }$$ estimates.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/405087987e161910b3fce29fc9d2825c5bad1928