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 language||English (US)|
|Number of pages||23|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Sep 20 2015|
ASJC Scopus subject areas
- Applied Mathematics