Skip to main content
SpringerLink
Log in

Smoothness of solutions of certain singular second-order equations

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

Abstract

Properties of solutions of a class of singular second-order equations are studied. It is proved that the smoothness of derivatives of a solution depends on the direction of differentiation. Inequalities analogous to those obtained by Shauder are derived for the second-order derivatives occurring in the equations.

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. A. M. Il'in, “A class of ultraparabolic equations,” Dokl. Akad. Nauk SSSR,159, No. 6, 1214–1217 (1964).

    Google Scholar 

  2. I. M. Sonin, “A class of diffusion processes,” Teoriya Veroyatn. i ee Primen.,12, No. 3, 540–547 (1967).

    Google Scholar 

  3. A. N. Kolmogorov. “Zufällige Bewegungen,” Ann. Math.,35, 116–117 (1934).

    Google Scholar 

  4. Ya. I. Shatyro, “Interior estimates for solutions of a class of ultraparabolic equations,” Matem. Zapiski Ural'skogo Un-ta,7, No. 4, 131–154 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Sverdlovsk Branch, Academy of Sciences of the USSR, USSR

    Ya. I. Shatyro

Authors
  1. Ya. I. Shatyro
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 101–111, July, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shatyro, Y.I. Smoothness of solutions of certain singular second-order equations. Mathematical Notes of the Academy of Sciences of the USSR 10, 484–489 (1971). https://doi.org/10.1007/BF01747076

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01747076

Search

Navigation