Now showing items 1-2 of 2
Weak convergence of reflecting Brownian motions
(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. Our theorem follows easily from known results and is perhaps known as a "folk law" among the specialists ...
A counterexample to the "hot spots" conjecture
(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 is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point ...