Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane

K. Astala, T. Iwaniec, G. Martin

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

The inequality of Alexandrov, Bakel'man and Pucci is a basic tool in the theory of linear elliptic partial differential equations (PDEs) which are not in divergence form as well as in the more general theory of nonlinear elliptic PDEs. Here, in two dimensions, we prove the sharp form of the maximum principle as conjectured by Pucci in 1966, give sharp forms of removable singularity results and prove a number of results for the degenerate elliptic setting. These results make use of the substantial recent advances in the planar theory of quasiconformal mappings.

Original languageEnglish (US)
Pages (from-to)49-74
Number of pages26
JournalJournal fur die Reine und Angewandte Mathematik
Issue number591
DOIs
StatePublished - Feb 24 2006

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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