Browsing Mathematics, Department of by Subject "Hot spots"
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(Princeton University and Institute for Advanced Study, 1999-01)We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions ...
(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.
(Institute of Mathematical Statistics, 1998-05-23)We will show that if a sequence of domains D [subscript] k increases to a domain D then the reflected Brownian motions in D [subscript] k's converge to the reflected Brownian motion in D, under mild technical assumptions. ...