## 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.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- 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