论文标题
$ c^{1，α} $规律性的统一方法的准抛物线方程
Unified approach to $C^{1,α}$ regularity for quasilinear parabolic equations
论文作者
论文摘要
在本文中，我们有兴趣获得$ c^{1，α} $估计的统一方法的弱解决方案，用于准线性抛物线方程，原型示例为\ [ u_t- \ text {div}（| \ nabla u |^{p -2} \ nabla u）= 0。\]，而无需分别考虑单数和退化案例。这是通过E.〜dibenedetto和A. friedman开发的新的缩放和微妙的适应来实现的。
In this paper, we are interested in obtaining a unified approach for $C^{1,α}$ estimates for weak solutions of quasilinear parabolic equations, the prototype example being \[ u_t - \text{div} (|\nabla u|^{p-2} \nabla u) = 0. \] without having to consider the singular and degenerate cases separately. This is achieved via a new scaling and a delicate adaptation of the covering argument developed by E.~DiBenedetto and A.~Friedman.
