几何中非线性椭圆与抛物方程的 $C^{2,\alpha}$ 正则性与估计
微分几何
2016-01-15 v3 偏微分方程分析
复变函数
摘要
在复几何与殆复几何中，假设解的 Laplacian 有界，我们给出了一些完全非线性椭圆和抛物方程解的尖锐 估计。我们还证明了关于具有锥形奇点的复 Monge-Amp\`{e}re 方程的类似结果。作为应用，我们获得了殆复几何中 Calabi-Yau 方程的局部估计。我们也改进了某些一致椭圆和抛物方程粘性解的 正则性与估计。关于 H"{o}lder 指数，我们所有的结果都是最优的。
引用
@article{arxiv.1410.3354,
title = {$C^{2,\alpha}$ regularities and estimates for nonlinear elliptic and parabolic equations in geometry},
author = {Jianchun Chu},
journal= {arXiv preprint arXiv:1410.3354},
year = {2016}
}
备注
22 pages, title changed, added parabolic version of main theorem (see section 5). This article has been accepted for publication on Calculus of Variations and Partial Differential Equations. This is accepted version. The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-015-0948-5