Boundary harnack principle for denjoy domains
Irina Popovici, Alexander L'vovich Vol'berg
Abstract
Irina Popovici, Alexander L'vovich Vol'berg
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.
OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
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