Partial regularity of solutions of fully nonlinear, Uniformly elliptic equations

Scott N. Armstrong, Luis E. Silvestre, Charles K. Smart

Research output: Contribution to journalArticlepeer-review


We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C 2,α on the complement of a closed set of Hausdorff dimension at most ε{lunate} less than the dimension. The equation is assumed to be C 1, and the constant ε{lunate} > 0 depends only on the dimension and the ellipticity constants. The argument combines the W 2,ε{lunate} estimates of Lin with a result of Savin on the C 2,α regularity of viscosity solutions that are close to quadratic polynomials.

Original languageEnglish (US)
Pages (from-to)1169-1184
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Issue number8
StatePublished - Aug 2012

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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