TY - JOUR
T1 - C2,α estimates for nonlinear elliptic equations in complex and almost complex geometry
AU - Tosatti, Valentino
AU - Wang, Yu
AU - Weinkove, Ben
AU - Yang, Xiaokui
N1 - Funding Information:
Research supported in part by NSF grants DMS-1236969, DMS-1308988 and DMS-1332196. The first named-author is supported in part by a Sloan Research Fellowship.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/9/20
Y1 - 2015/9/20
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-014-0791-0
DO - 10.1007/s00526-014-0791-0
M3 - Article
AN - SCOPUS:84939471020
SN - 0944-2669
VL - 54
SP - 431
EP - 453
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
ER -