C2,α regularities and estimates for nonlinear elliptic and parabolic equations in geometry

Jianchun Chu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We give sharp C2,α estimates for solutions of some fully nonlinear elliptic and parabolic equations in complex geometry and almost complex geometry, assuming a bound on the Laplacian of the solution. We also prove the analogous results to complex Monge–Ampère equations with conical singularities. As an application, we obtain a local estimate for Calabi–Yau equation in almost complex geometry. We also improve the C2,α regularities and estimates for viscosity solutions to some uniformly elliptic and parabolic equations. All our results are optimal regarding the Hölder exponent.

Original languageEnglish (US)
Article number8
Pages (from-to)1-20
Number of pages20
JournalCalculus of Variations and Partial Differential Equations
Volume55
Issue number1
DOIs
StatePublished - Feb 1 2016

Keywords

  • 32Q60
  • 32W20
  • 35J60
  • 35K55
  • 53C55
  • 58J05

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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