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Parabolic interior Schauder estimates by the maximum principle

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Abstract

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 2x u is Hölder continuous in t (exponent α/2) even if the coefficients and nonhomogeneous term are not.

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References

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Authors and Affiliations

  1. University of Kentucky, Lexington, Kentucky

    Barry F. Knerr

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  1. Barry F. Knerr
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Communicated by J. Serrin

Note. The author is currently at Bell Laboratories in Naperville, Illinois.

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Knerr, B.F. Parabolic interior Schauder estimates by the maximum principle. Arch. Rational Mech. Anal. 75, 51–58 (1980). https://doi.org/10.1007/BF00284620

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  • DOI: https://doi.org/10.1007/BF00284620

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