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W super(2,1) regularity for solutions of the Monge-Ampere equation

Inventiones mathematicae, 2013-04, Vol.192 (1), p.55-69 [Peer Reviewed Journal]

ISSN: 0020-9910 ;EISSN: 1432-1297 ;DOI: 10.1007/s00222-012-0405-4

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  • Title:
    W super(2,1) regularity for solutions of the Monge-Ampere equation
  • Author: De Philippis, Guido ; Figalli, Alessio
  • Subjects: Estimates
  • Is Part Of: Inventiones mathematicae, 2013-04, Vol.192 (1), p.55-69
  • Description: In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Ampere equation, with right-hand side bounded away from zero and infinity, is $W2,1}_{\mathrm{loc}}$. This is obtained by showing higher integrability a priori estimates for D super(2) u, namely D super(2) uLlog super( )kL for any k.
  • Language: English
  • Identifier: ISSN: 0020-9910
    EISSN: 1432-1297
    DOI: 10.1007/s00222-012-0405-4
  • Source: AUTh Library subscriptions: ProQuest Central
    Alma/SFX Local Collection
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