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Wiener's criterion for parabolic equations with variable coefficients and its consequences


Authors: Nicola Garofalo and Ermanno Lanconelli
Journal: Trans. Amer. Math. Soc. 308 (1988), 811-836
MSC: Primary 35K20; Secondary 31B10, 31B20
DOI: https://doi.org/10.1090/S0002-9947-1988-0951629-2
MathSciNet review: 951629
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Abstract: In a bounded set in $ {{\mathbf{R}}^{n + 1}}$ we study the problem of the regularity of boundary points for the Dirichlet problem for a parabolic operator with smooth coefficients. We give a geometric characterization, modelled on Wiener's criterion for Laplace's equation, of those boundary points that are regular. We also present some important consequences. Here is the main one: a point is regular for a variable coefficient operator if and only if it is regular for the constant coefficient operator obtained by freezing the coefficients at that point.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1988-0951629-2
Keywords: Parabolic equations, Wiener's criterion, mean value properties
Article copyright: © Copyright 1988 American Mathematical Society

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