Domains of finite type and holder continuity of the perron-bremermann function

Dan Coman

doi:10.1090/s0002-9939-97-04100-2

Domains of finite type and holder continuity of the perron-bremermann function

Dan Coman

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Let Ω be a smoothly bounded domain in ℂ™ such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω at 0 in terms of the Hölder exponent of its Perron-Bremermann function with simple boundary data. We then use this to show that a smoothly bounded domain in ℂ² is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Holder continuous boundary data is Hölder continuous.

Original language	English (US)
Pages (from-to)	3569-3574
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	125
Issue number	12
DOIs	https://doi.org/10.1090/s0002-9939-97-04100-2
State	Published - 1997
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "Let Ω be a smoothly bounded domain in ℂ{\texttrademark} such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω at 0 in terms of the H{\"o}lder exponent of its Perron-Bremermann function with simple boundary data. We then use this to show that a smoothly bounded domain in ℂ2 is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Holder continuous boundary data is H{\"o}lder continuous.",

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AB - Let Ω be a smoothly bounded domain in ℂ™ such that 0 ∈ ∂Ω. We give a bound for the type of ∂Ω at 0 in terms of the Hölder exponent of its Perron-Bremermann function with simple boundary data. We then use this to show that a smoothly bounded domain in ℂ2 is pseudoconvex of finite type if and only if its Perron-Bremermann function corresponding to Holder continuous boundary data is Hölder continuous.

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ER -

Domains of finite type and holder continuity of the perron-bremermann function

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