In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, with right hand side bounded away from zero and infinity, is W2,1loc. This is obtained by showing higher integrability a-priori estimates for D2u, namely D2u∈LlogkL for any k∈N.

W^{2,1}- regularity for solutions of the Monge-Ampere equation

De Philippis, Guido;
2013-01-01

Abstract

In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, with right hand side bounded away from zero and infinity, is W2,1loc. This is obtained by showing higher integrability a-priori estimates for D2u, namely D2u∈LlogkL for any k∈N.
2013
192
1
55
69
https://arxiv.org/abs/1111.7207
De Philippis, Guido; Figalli, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15848
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