Skip to main content
SpringerLink
Log in

Rearrangements of differentiable functions

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

An investigation of properties of rearrangements of functions differentiable in a generalized sense. Lower bounds are obtained for the symmetric norm of the gradient of a function. Analogous relations are established for the simplest functional of the calculus of variations.

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

Similar content being viewed by others

Literature cited

  1. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities [Russian translation], Moscow (1948).

  2. V. S. Klimov, “Imbedding theorems for symmetric spaces,” Matem. Sb.,79, No. 2, 171–179 (1969).

    Google Scholar 

  3. S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Moscow (1969).

  4. W. H. Fleming and R. Rishel, “An integral formula for total gradiant variation,” Arch. Math.,11, No. 3, 218–222 (1960).

    Google Scholar 

  5. DeGiorgi, “Su una teoria generalle della misure (n−1)-dimensionale in uno spazio ad r dimensioni,” Ann. Mat. Pura ed. Appl. (4),36, 191–213 (1954).

    Google Scholar 

  6. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Moscow (1964).

  7. E. M. Semenov, “Imbedding theorems for Banach spaces of measurable functions,” Dokl. AN SSSR,156, No. 6, 1292–1295 (1964).

    Google Scholar 

  8. P. P. Zabreiko, “Nonlinear integral operators,” Trans. of a Seminar on Functional Analysis [in Russian], No. 8, Voronezh (1966), pp. 3–148.

    Google Scholar 

  9. M. A. Krasnosel'skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Moscow (1958).

  10. G. Polya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics [Russian translation], Moscow (1962).

Download references

Author information

Authors and Affiliations

  1. Novocherkassk Polytechnic Institute, USSR

    V. S. Klimov

Authors
  1. V. S. Klimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 9, No. 6, pp. 629–638, June, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klimov, V.S. Rearrangements of differentiable functions. Mathematical Notes of the Academy of Sciences of the USSR 9, 365–370 (1971). https://doi.org/10.1007/BF01094577

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01094577

Keywords

Search

Navigation