二阶椭圆与抛物方程的偏Schauder估计

Partial Schauder estimates for elliptic and parabolic equations of second order

Schauder估计是偏微分方程正则性理论的主要结论之一,它在研究非线性方程解的存在唯一性中起到了非常重要的作用.关于各向异性方程的偏Schauder估计是近年来的研究热点之一,本文旨在介绍几类二阶椭圆和抛物方程的偏Schauder估计及其证明思路.本文还给出了散度型椭圆方程偏Schauder估计的一个新的证明.

As a branch of regularity, Schauder estimate plays a very important role in proving existence and uniqueness for the nonlinear elliptic and parabolic equations. In recent years, there are a number of works concerning Schauder estimate of anisotropic equations. In this review, we aim to introduce some results about anisotropic Schauder estimate for elliptic and parabolic equations.