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Boundary property of n-dimensional mappings with bounded distortion

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Abstract

The following assertion is proved: letf:B→Rn be an arbitrary (in general, not single-sheeted) mapping with bounded distortion of an n-dimensional sphere B, satisfying the conditions: A) the setf(B) is bounded; B) the partial derivatives\((i,\frac{{\partial fi}}{{\partial xj}}(i,j = 1,2,...,n)\) are summable with respect to B with degreeα (1< α <- n). Then the mappingf has angular boundary values everywhere on the boundary of the sphere with the possible exception of a set ofα-capacity zero.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Academy of Sciences of the Ukrainian SSR, USSR

    V. M. Miklyukov

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  1. V. M. Miklyukov
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Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 159–164, February, 1972.

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Miklyukov, V.M. Boundary property of n-dimensional mappings with bounded distortion. Mathematical Notes of the Academy of Sciences of the USSR 11, 102–105 (1972). https://doi.org/10.1007/BF01097925

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  • DOI: https://doi.org/10.1007/BF01097925

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