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The Boundary Harnack Principle for Non‐Divergence form Elliptic Operators
Author(s) -
Bass Richard F.,
Burdzy Krzysztof
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/50.1.157
Subject(s) - harnack's inequality , harnack's principle , counterexample , mathematics , boundary (topology) , harmonic function , divergence (linguistics) , mathematical analysis , elliptic operator , operator (biology) , domain (mathematical analysis) , order (exchange) , hölder condition , pure mathematics , harmonic , physics , discrete mathematics , finance , linguistics , philosophy , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , economics , gene
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 α if α > 1 2 . A counterexample shows that 1 2 is sharp. For Hölder domains of order α with α∈(0,1], the boundary Harnack principle holds provided the domain also satisfies a strong uniform regularity condition.