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Journal of the London Mathematical Society 1994 50(1):157-169; doi:10.1112/jlms/50.1.157
© 1994 by London Mathematical Society
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© The London Mathematical Society

The Boundary Harnack Principle for Non-Divergence form Elliptic Operators

Richard F. Bass and Krzysztof Burdzy

Department of Mathematics, University of Washington Seattle, Washington 98195, USA

Received 12 June 1991.

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} > Formula. A counterexample shows that Formula is sharp. For Hölder domains of order {alpha} with {alpha}isin(0,1], the boundary Harnack principle holds provided the domain also satisfies a strong uniform regularity condition.

Research partially supported by NSF grants DMS 8822053 and DMS 8901255.


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