非线性抛物方程古典解的一个先验估计

A Priori Estimates for Classical Solutions of Fully Non-linear Parabolic Equations

给定常数0<β<1,假定非线性算子F几乎处处是局部c^1,β的,本文研究了完全非线性抛物方程的ut-f(D^2xu)=0古典解的性质。如果上述方程的古典解的二阶导数有一个连续模ρ,证明了其解的一个内部C^2,a估计,这里α是一个仅依赖于非线性算子F的常数。

For the fully nonlinear uniformly parabolic equations ut-f(D^2xu)=0;.It is well known that the viscosity solutions are of C^2,a if the nonlinear operators are convex (or concave). In this paper, we study the classical solution for the fully nonlinear parabolic equations, where the nonlinear operators F is local c^1,β almost everywhere for 0<β<1.It will be shown the interior C^2,a regularity of the classical solutions provided there exists a function ρ that is a continuous modulus of second order derivatives of the classical solution.