Higher Integrability for Minimizers of the Mumford-Shah Functional

Guido de Philippis, Alessio Figalli

Research output: Contribution to journalArticlepeer-review


We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi (Free discontinuity problems in calculus of variations. Frontiers in pure and applied mathematics, North-Holland, Amsterdam, pp 55-62, 1991).

Original languageEnglish (US)
Pages (from-to)491-502
Number of pages12
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - Aug 2014

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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