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 language||English (US)|
|Number of pages||20|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Feb 1 2016|
ASJC Scopus subject areas
- Applied Mathematics