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

Sevost′yanov, E.

doi:10.1090/spmj/1579

Boundary behavior and equicontinuity for families of mappings in terms of prime ends
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by E. A. Sevost′yanov
Translated by: S. V. Kislyakov

St. Petersburg Math. J. 30 (2019), 973-1005

DOI: https://doi.org/10.1090/spmj/1579

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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