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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Boundary behavior and equicontinuity for families of mappings in terms of prime ends

Author: E. A. Sevost′yanov
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 30 (2018), nomer 6.
Journal: St. Petersburg Math. J. 30 (2019), 973-1005
MSC (2010): Primary 30C64; Secondary 30D40
Published electronically: September 16, 2019
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Abstract: The boundary behaviour is treated for classes of mappings that are related to the study of Sobolev and Sobolev-Orlicz spaces in the $ n$-dimensional Euclidean space. Continuous extendibility to the boundary of a regular domain is studied for such classes in terms of prime ends. Moreover, the global behavior of families of such mappings is investigated, in particular, again in terms of prime ends, some results are proved concerning the equicontinuity of such families.

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Additional Information

E. A. Sevost′yanov
Affiliation: Zhytomyr Ivan Franko State University, ul. Bol′shaya Berdichevskaya 40, 10008 Zhitomir, Ukraine

Keywords: Moduli of families of curves and surfaces, mappings with bounded or finite distorsion, boundary behavior of mappings, prime ends of spacial domains
Received by editor(s): January 25, 2017
Published electronically: September 16, 2019
Article copyright: © Copyright 2019 American Mathematical Society