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.File in questo prodotto:
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2013_W 2,1 regularity for solutions of the Monge?Ampe?re equation.pdf
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