Comparison of potential theoretic properties of rough domains |
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| Authors: | Krzysztof Burdzy Zhen-Qing Chen |
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| Affiliation: | Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98115-4350 ; Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98115-4350 |
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| 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  . |
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| Keywords: | Neumann Laplacian trap domain intrinsic ultracontractivity parabolic Harnack principle. |
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