热传导方程解的部分Schauder估计

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 307-312.

热传导方程解的部分Schauder估计

巴娜, 郑列

湖北工业大学理学院武汉 430068

收稿日期:2016-07-12 修回日期:2016-12-24 出版日期:2017-04-26 发布日期:2017-04-26
通讯作者: 巴娜 E-mail:bana1002@126.com
作者简介:郑列,Teacherzhenglie@hotmail.com
基金资助:
湖北省教育厅科研项目（Q20151401）

Partial Schauder Estimates for the Heat Equation

Ba Na, Zheng Lie

School of Science, Hubei University of Technology, Wuhan 430068

Received:2016-07-12 Revised:2016-12-24 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the Scientific Research Project of Education Department of Hubei Province (Q20151401)

摘要/Abstract

摘要： 该文主要研究热传导方程的解u的部分正则性，得到了u的部分Schauder估计的积分形式的统一表达式，即当非齐次项f关于某一个方向Lipschitz连续，Hölder连续或者Dini连续时，部分Schauder估计均可由该表达式推出.特别地，当方程的非齐次项f沿x_n方向Hölder连续时，混合偏导数u_{xx_n}是Hölder连续的.

关键词: 热传导方程, 部分正则性, 部分Schauder估计

Abstract: In this paper, we study the partial regularity of solutions to the heat equation. The resulting partial Schauder estimates have a unified integral-typed expression, from which the known interior Schauder estimates can be derived when the nonhomogeneous term f(x,t) is Lipschitz continuous, Hölder continuous or Dini continuous respectively in a certain direction. In particular, when f(x,t) is Hölder continuous in the direction x_n, so are the mixed derivatives u_{xx_n} with the same Hölder index.

Key words: Heat equation, Partial regularity, Partial Schauder estimates

中图分类号:

O175.26

巴娜, 郑列. 热传导方程解的部分Schauder估计[J]. 数学物理学报, 2017, 37(2): 307-312.

Ba Na, Zheng Lie. Partial Schauder Estimates for the Heat Equation[J]. Acta mathematica scientia,Series A, 2017, 37(2): 307-312.

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