Browsing Mathematics, Department of by Subject "boundary Harnack principle"
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The boundary Harnack principle for nondivergence 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 ... 
A boundary Harnack principle in twisted Hölder domains
(Annals of Mathematics, 199109)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 ... 
Hölder domains and the boundary Harnack principle
(Duke University Press, 199110)A version of the boundary Harnack principle is proven. 
A probabilistic proof of the boundary Harnack principle
(Birkhauser Boston, Inc., 1990)The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy ...