Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (2): 307-312.

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Partial Schauder Estimates for the Heat Equation

Ba Na, Zheng Lie   

  1. 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)

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 xn, so are the mixed derivatives uxxn with the same Hölder index.

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

CLC Number: 

  • O175.26
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