Skip to main content
SpringerLink
Log in

Sobolev-type classes of functions with values in a metric space

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. S. L. Sobolev, “On a certain boundary value problem for polyharmonic equations,” Mat. Sb.,2, 467–500 (1937).

    Google Scholar 

  2. S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  3. O. V. Besov, V. P. Il’in, and C. M. Nikol’skiî, Integral Representations and Embedding Theorems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  4. V. G. Maz’ya, Sobolev Spaces [in Russian], Leningrad Univ., Leningrad (1985).

    Google Scholar 

  5. H. Triebel, Interpolation Theory. Function Spaces. Differential Operators, VEB Deutsch. Verlag Wissensch., Berlin (1978).

    Google Scholar 

  6. V. M. Gol’dshtein and Yu. G. Reshetnyak, Quasiconformal Mappings and Sobolev Spaces, Kluwer, Dordrecht, Boston, and London (1990).

    MATH  Google Scholar 

  7. N. J. Korevaar and R. M. Schoen, “Sobolev spaces and harmonic maps for metric space targets,” Comm. Anal. Geom.,1, No. 4, 1–99 (1993).

    Google Scholar 

  8. L. Ambrosio, “Metric space valued functions of bounded variation,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),17, No. 3, 439–478 (1990).

    MATH  Google Scholar 

  9. A. D. Alexandrov, “On a generalization of Riemannian geometry,” in: Selected Works. Part I, Gordon and Breach Publishers, Amsterdam etc., 1996, pp. 187–249.

    Google Scholar 

  10. P. Hajłasz, “Sobolev spaces on an arbitrary metric space,” Potential Anal.,5, No. 4, 403–415 (1996).

    Google Scholar 

  11. M. Biroli and U. Mosco, “Sobolev and isoperimetric inequalities for Dirichlet forms in homogeneous spaces,” Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.,9, No. 6, 37–44 (1995).

    Google Scholar 

  12. L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis in Partially Ordered Spaces [in Russian], Gostekhizdat, Moscow and Leningrad (1950).

    Google Scholar 

  13. Yu. G. Reshetnyak, Space Mappings with Bounded Distortion, Amer. Math. Soc., Providence (1989).

    MATH  Google Scholar 

  14. Yu. G. Reshetnyak, “General theorems on semicontinuity and convergence with a functional,” Sibirsk. Mat. Zh.,8, No. 3, 1051–1069 (1967).

    Google Scholar 

  15. Yu. G. Reshetnyak, “Generalized derivatives and differentiability almost everywhere,” Dokl. Akad. Nauk SSSR,170, No. 6, 1273–1275 (1966).

    Google Scholar 

  16. V. P. Il’in, “On an embedding theorem for a limit exponent,” Dokl. Akad. Nauk SSSR,96, No. 5, 905–908 (1954).

    MATH  Google Scholar 

Download references

Authors
  1. Yu. G. Reshetnyak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research was supported by the Russian Foundation for Basic Research (Grant 96-01-01769).

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 3, pp. 657–675, May–June, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reshetnyak, Y.G. Sobolev-type classes of functions with values in a metric space. Sib Math J 38, 567–583 (1997). https://doi.org/10.1007/BF02683844

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02683844

Keywords

Search

Navigation