Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

  • A. A. Vasil’eva
Article

DOI: 10.1134/S1061920809040098

Cite this article as:
Vasil’eva, A.A. Russ. J. Math. Phys. (2009) 16: 543. doi:10.1134/S1061920809040098
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Abstract

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted Lp space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted Lp-space.

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • A. A. Vasil’eva
    • 1
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia