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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Comparison of potential theoretic properties of rough domains
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by Krzysztof Burdzy and Zhen-Qing Chen PDF
Proc. Amer. Math. Soc. 134 (2006), 3247-3253 Request permission

Abstract:

We discuss the relationships between the notions of intrinsic ultracontractivity, the parabolic Harnack principle, compactness of the 1-resolvent of the Neumann Laplacian, and the non-trap property for Euclidean domains with finite Lebesgue measure. In particular, we give an answer to an open problem raised by Davies and Simon in 1984 about the possible relationship between intrinsic ultracontractivity for the Dirichlet Laplacian in a domain $D$ and compactness of the 1-resolvent of the Neumann Laplacian in $D$.
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Additional Information
  • Krzysztof Burdzy
  • Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98115-4350
  • Email: burdzy@math.washington.edu
  • Zhen-Qing Chen
  • Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98115-4350
  • MR Author ID: 242576
  • ORCID: 0000-0001-7037-4030
  • Email: zchen@math.washington.edu
  • Received by editor(s): May 17, 2005
  • Published electronically: June 6, 2006
  • Additional Notes: This research was partially supported by NSF grant DMS-0303310.
  • Communicated by: Michael T. Lacey
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3247-3253
  • MSC (2000): Primary 35P05; Secondary 60J45
  • DOI: https://doi.org/10.1090/S0002-9939-06-08685-0
  • MathSciNet review: 2231908