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Traps for Reflected Brownian Motion

Show simple item record Burdzy, Krzysztof Chen, Zhen-Qing Marshall, Donald E. 2005-10-17T17:28:28Z 2005-10-17T17:28:28Z 2005-08-16
dc.identifier.citation Mathematische Zeitschrift en
dc.description.abstract Consider an open set D [is an element of the set] R [The set of Real Numbers] [superscript]d, d [is greater than or equal to] 2, and a closed ball B [is a proper subset of] D. Let E[superscript]xT[subscript]B denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x [is an element of the set] D. We say that D is a trap domain if sup[subscript]x E[superscript]xT[subscript]B = [infinity]. We fully characterize simply connected planar trap domains using a geometric condition. We give a number of (less complete) results for multidimensional domains. We discuss the relationship between trap domains and some other potential theoretic properties of D such as compactness of the 1-resolvent of the Neumann Laplacian. In addition, 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. en
dc.description.sponsorship National Science Foundation (NSF) en
dc.format.extent 315390 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.publisher Springer-Verlag GmbH en
dc.subject Reflecting Brownian motion en
dc.subject Neumann Laplacian en
dc.subject Hitting time en
dc.subject Sobolev space en
dc.subject Conformal mapping en
dc.subject Hyperbolic distance en
dc.subject Intrinsic ultracontractivity en
dc.subject Parabolic Harnack principle en
dc.title Traps for Reflected Brownian Motion en
dc.type Article en

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