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A Strong Regularity Result for Parabolic Equations

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Abstract

We consider a parabolic equation with a drift term Δu+b∇u−u t =0. Under the condition div b=0, we prove that solutions possess dramatically better regularity than those provided by standard theory. For example, we prove continuity of solutions when not even boundedness is expected.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Riverside, CA 92521, USA

    Qi S. Zhang

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  1. Qi S. Zhang
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Correspondence to Qi S. Zhang.

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Communicated by B. Simon

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Zhang, Q. A Strong Regularity Result for Parabolic Equations. Commun. Math. Phys. 244, 245–260 (2004). https://doi.org/10.1007/s00220-003-0974-6

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  • DOI: https://doi.org/10.1007/s00220-003-0974-6

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