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

Garofalo, Nicola; Lanconelli, Ermanno

doi:10.1090/S0002-9947-1988-0951629-2

Wiener’s criterion for parabolic equations with variable coefficients and its consequences
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by Nicola Garofalo and Ermanno Lanconelli PDF

Trans. Amer. Math. Soc. 308 (1988), 811-836 Request permission

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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