Geodesic
Necessary and sufficient conditions $(\alpha,\beta)$-accessibility of domain in nonsmooth case
Problemy analiza, Tome 4 (2015) no. 2, pp. 3-11.

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In [1], [2] $(\alpha,\beta)$-accessible domains in $\mathbb{C}$ were defined and investigated, and the criterion of $(\alpha,\beta)$-accessibility in a smooth case was obtained. $(\alpha,\beta)$-accessible domains are starlike, $\gamma$-accessible ($\gamma=\min\{\alpha;\beta\}$), 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 $(\alpha,\beta)$-accessibility of domain in nonsmooth case.
Keywords: cone condition.
Mots-clés : $\alpha$-accessible domain, $(\alpha,\beta)$-accessible domain 
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K. F. Amozova. Necessary and sufficient conditions $(\alpha,\beta)$-accessibility of domain in nonsmooth case. Problemy analiza, Tome 4 (2015) no. 2, pp. 3-11. http://geodesic.mathdoc.fr/item/PA_2015_4_2_a0/

[1] Anikiev A. N., “Plane domains with special cone condition”, Russian Mathematics, 58:2 (2014), 62–63 | DOI | MR | Zbl

[2] Anikiev A. N., “Plane domains with special cone condition”, Probl. Anal. Issues Anal., 3(21):1 (2014), 16–31 | DOI | MR | Zbl

[3] Amozova K. F., Ganenkova E. G., “About planar $(\alpha, \beta)$-accessible domains”, Probl. Anal. Issues Anal., 3(21):2 (2014), 3–15 | DOI | MR | Zbl

[4] Liczberski P., Starkov V. V., “Domains in $\mathbb{R}^n$ with conical accessible boundary”, J. Math. Anal. Appl., 408:2 (2013) | DOI | MR | Zbl

[5] Amozova K. F., Starkov V. V., “$\alpha$-accessible domains, a nonsmooth case”, Izv. Sarat. Univ. N. S. Ser. Math. Mech. Inform., 13:3 (2013) (in Russian)

[6] Amozova K. F., “Sufficient conditions of $\alpha$-accessibility of domain in nonsmooth case”, Probl. Anal. Issues Anal., 2(20):1 (2013) (in Russian) | DOI | MR | Zbl