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

作者: 曹 毅 * , 王治国 :陕西师范大学数学与信息科学学院;

关键词: 完全非线性一致抛物古典解Nonlinear Uniformly Parabolic Classical Solutions

摘要: 给定常数,假定非线性算子F几乎处处是局部的,本文研究了完全非线性抛物方程的古典解的性质。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估计,这里α是一个仅依赖于非线性算子F的常数。

Abstract: For the fully nonlinear uniformly parabolic equations .It is well known that the viscosity solutions are of 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 almost everywhere for .It will be shown the interiorregularity of the classical solutions provided there exists a function ρ that is a continuous modulus of second order derivatives of the classical solution.

文章引用: 曹 毅 , 王治国 (2012) 非线性抛物方程古典解的一个先验估计。 理论数学, 2, 249-255. doi: 10.12677/PM.2012.24038

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