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Article contents
A counterexample in parabolic potential theory
Part of:
Parabolic equations and systems
Published online by Cambridge University Press: 26 February 2010
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
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- Copyright
- Copyright © University College London 1995
References
1.Deny, J.. Un theoreme sur les ensembles effilés. Ann. Univ. Grenoble Sect. Sci. Math. Phys., 23 (1948), 139–142.Google Scholar
2.Doob, J. L.. Classical potential theory and its probabilistic counter part (Springer: New York, 1984).Google Scholar
3.Friedman, A.. Partial differential equations of parabolic type (Prentice Hall: Englewood Cliffs, N.J., 1964).Google Scholar
5.Kaufman, R. and Wu, J. M.. Singularity of parabolic measures. Comp. Math., 40 (1980), 243–250.Google Scholar
6.Kaufman, R. and Wu, J. M.. Parabolic potential theory. J. Diff. Eq., 43 (1982) 204–234.Google Scholar
7.Stroock, D. W. and Varadhan, S. R. S.. Multidimensional diffusion processes (Springer: Berlin, 1979).Google Scholar
8.Watson, N. A.. Thinness and boundary behaviour of potentials for the heat equation. Mathematika, 32 (1985) 90–95.Google Scholar