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    On the "hot spots" conjecture of J. Rauch 

    Burdzy, Krzysztof; Banuelos, Rodrigo (Academic Press (Elsevier), 1999-05-10)
    We will state several rigorous versions of J. Rauch's "hot spots" conjecture, review some known results, and prove the conjecture under some additional assumptions. Let us, however, first observe that the conclusion cannot hold for all initial conditions.
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    Erratum to The Supremum of Brownian Times on Hölder Curves 

    Bass, Richard F.; Burdzy, Krzysztof (Birkhauser, 2002-05-21)
    For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all functions whose Hölder norm of order [sigma] is less than or equal to 1. We show that the supremum of L ...
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    On the Robin problem in fractal domains 

    Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing (2005)
    We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other families of domains where it is equal to 0. We also give a new result on "trap domains" defined in [BCM], i.e., domains where reflecting ...
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    Neumann eigenfunctions and Brownian couplings 

    Burdzy, Krzysztof (Mathematical Society of Japan, 2004)
    This is a review of research on geometric properties of Neumann eigenfunctions related to the "hot spots" conjecture of Jeff Rauch. The paper also presents, in an informal way, some probabilistic techniques used in the proofs.
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    Burdzy, Krzysztof (84)
    Bass, Richard F. (21)Chen, Zhen-Qing (13)Holyst, Robert (7)Frankel, David M. (4)Banuelos, Rodrigo (3)Barlow, Martin T. (3)Kaspi, Haya (3)Khoshnevisan, Davar (3)Marshall, Donald E. (3)... View MoreSubjectBrownian motion (32)local time (7)diffusion (6)Neumann eigenfunctions (5)boundary Harnack principle (4)conditioned Brownian motion (4)Hölder domains (4)iterated Brownian motion (4)eigenfunction (3)eigenvalues (3)... View MoreDate Issued2000 - 2005 (36)1990 - 1999 (44)1989 - 1989 (4)

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