NECESSARY AND SUFFICIENT CONDITIONS OF (α, β)-ACCESSIBILITY OF DOMAIN IN NONSMOOTH CASE
In [1], [2] (α, β)-accessible domains in C were defined and investigated, and the criterion of (α, β)-accessibility in a smooth case was obtained. (α, β)-accessible domains are starlike, γ-accessible (γ = min{α, β}), and satisfy the so-called “cone condition” (i. e. the domains are conically access...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2015-12-01
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| Series: | Проблемы анализа |
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| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=2950&lang=en |
| Summary: | In [1], [2] (α, β)-accessible domains in C were defined and investigated, and the criterion of (α, β)-accessibility in a smooth case was obtained. (α, β)-accessible domains are starlike, γ-accessible (γ = min{α, β}), and satisfy the so-called “cone condition” (i. e. the domains are conically accessible from the interior), which is important for applications, such as the theory of integral representations of functions, imbedding theorems, the questions of the boundary behavior of functions, the solvability of Dirichlet problem. In this paper the author obtains the necessary and some sufficient conditions of (α, β)-accessibility of domain in nonsmooth case. |
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| ISSN: | 2306-3424 2306-3432 |