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A counterexample in parabolic potential theory

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  26 February 2010

Pawel Kröger
Pawel Kröger
Affiliation:
Mathematisches Institut, Bismarchstr. 1 1/2, 91054 Erlangen, Germany.
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Extract

In Section 1 of this note we will construct an example of a subset of R × Rn such that the parabolic capacity with respect to the heat equation is zero although its orthogonal projection onto {0} × Rn is the whole space. Such examples were already given by R. Kaufman and J.-M. Wu in [5] and [6]. However, our probabilistic approach seems to be more transparent since it does not depend on explicit formulas for Green functions.

MSC classification

Secondary: 35K05: Heat equation
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 392 - 396
Copyright
Copyright © University College London 1995

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References

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