Now showing items 1-4 of 4
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 ...
Hölder domains and the boundary Harnack principle
(Duke University Press, 1991-10)
A version of the boundary Harnack principle is proven.
A boundary Harnack principle in twisted Hölder domains
(Annals of Mathematics, 1991-09)
The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the set] (0, 1/2), there exists a twisted Hölder domain of order [alpha] for which the boundary Harnack principle ...
The boundary Harnack principle for non-divergence form elliptic operators
(Cambridge University Press, 1994)
If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows that 1/2 is sharp. For Hölder domains of order [alpha] with [alpha is an element of the set] (0, 1], the ...