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#### 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 ...

#### 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 ...

#### 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 corollary of Theorem 1.1. The boundary Harnack principle may be viewed as a Harnack inequality for ...