1998•Complex Variables Theory and Application An International JournalRequires access

Boundary harnack principle for denjoy domains

Irina Popovici, Alexander L'vovich Vol'berg

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Abstract

In this paper we are condidering positive, symmetric, harmonic functions in a Denjoy domain with uniformly perfect boundary that vanish continuously on the boundary of that domain. Given two such functions ν, υ we are proving that the ratio (ν/υ) can be extended to the boundary, and the extension is Holder continuous with exponent depending on the uniformly perfectness cnstants of the bundary.

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What this paper is about

In this paper we are condidering positive, symmetric, harmonic functions in a Denjoy domain with uniformly perfect boundary that vanish continuously on the boundary of that domain. Given two such functions ν, υ we are proving that the ratio (ν/υ) can be extended to the boundary, and the extension is Holder continuous with exponent depending on the uniformly perfectness cnstants of the bundary.

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Available abstract

In this paper we are condidering positive, symmetric, harmonic functions in a Denjoy domain with uniformly perfect boundary that vanish continuously on the boundary of that domain. Given two such functions ν, υ we are proving that the ratio (ν/υ) can be extended to the boundary, and the extension is Holder continuous with exponent depending on the uniformly perfectness cnstants of the bundary.

Key concepts: Mathematics, Harmonic function, Harnack's principle, Harnack's inequality, Boundary (topology), Harmonic measure, Domain (mathematical analysis), Mathematical analysis

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