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Hölder domains and the boundary Harnack principle
(Duke University Press, 1991-10)
A version of the boundary Harnack principle is proven.
A representation of local time for Lipschitz surfaces
(Springer-Verlag GmbH, 1990)
Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with diameter greater than r which started before time t. Then rN[subscript]t(r) converges as r --> 0 to a ...
On the "hot spots" conjecture of J. Rauch
(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.