On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian

Fernando Charro, Guido de Philippis, Agnese Di Castro, Davi Máximo

Research output: Contribution to journalArticlepeer-review


We prove L bounds and estimates of the modulus of continuity of solutions to the Poisson problem for the normalized infinity and p-Laplacian, namely, We are able to provide a stable family of results depending continuously on the parameter p. We also prove the failure of the classical Alexandrov-Bakelman-Pucci estimate for the normalized infinity Laplacian and propose alternate estimates.

Original languageEnglish (US)
Pages (from-to)667-693
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Issue number3-4
StatePublished - Nov 2013

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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