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Comparison of potential theoretic properties of rough domains
Author(s):
Krzysztof
Burdzy;
Zhen-Qing
Chen
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3247-3253.
MSC (2000):
Primary 35P05;
Secondary 60J45
Posted:
June 6, 2006
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Abstract |
References |
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Additional information
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  and compactness of the 1-resolvent of the Neumann Laplacian in  .
References:
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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
Email:
zchen@math.washington.edu
DOI:
10.1090/S0002-9939-06-08685-0
PII:
S 0002-9939(06)08685-0
Keywords:
Neumann Laplacian,
trap domain,
intrinsic ultracontractivity,
parabolic Harnack principle.
Received by editor(s):
May 17, 2005
Posted:
June 6, 2006
Additional Notes:
This research was partially supported by NSF grant DMS-0303310.
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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