C2,α estimates for nonlinear elliptic equations in complex and almost complex geometry

Valentino Tosatti, Yu Wang, Ben Weinkove*, Xiaokui Yang

*Corresponding author for this work

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

We describe how to use the perturbation theory of Caffarelli to prove Evans–Krylov type C2,α estimates for solutions of nonlinear elliptic equations in complex geometry, assuming a bound on the Laplacian of the solution. Our results can be used to replace the various Evans–Krylov type arguments in the complex geometry literature with a sharper and more unified approach. In addition, our methods extend to almost-complex manifolds, and we use this to obtain a new local estimate for an equation of Donaldson.

Original languageEnglish (US)
Pages (from-to)431-453
Number of pages23
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number1
DOIs
StatePublished - Sep 20 2015

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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