Parabolic interior Schauder estimates by the maximum principle

  • Barry F. Knerr


In [1] Brandt proved all of the assertions of the parabolic interior Schauder estimates regarding Hölder continuity in x (exponent α) by a very simple maximum principle argument. In this paper we give a simple maximum principle proof of Hölder continuity in t (exponent α/2). In fact we show that each derivative D x 2 u is Hölder continuous in t (exponent α/2) even if the coefficients and nonhomogeneous term are not.


Neural Network Complex System Nonlinear Dynamics Maximum Principle Electromagnetism 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Barry F. Knerr
    • 1
  1. 1.University of KentuckyLexington

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