Skip to main content
Log in

Smoothness of solutions to the Dirichlet problem for a second-order elliptic equation with a square integrable boundary function

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. E. DeGiorgi, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 3, 25–43 (1957).

    Google Scholar 

  2. J. Nash, Am. J. Math. 80, 931–954 (1958).

    Article  MATH  Google Scholar 

  3. J. Moser, Commun. Pure Appl. Math. 17, 101–134 (1964).

    Article  MATH  Google Scholar 

  4. O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics (Nauka, Moscow, 1973; Springer-Verlag, New York, 1985).

    Google Scholar 

  5. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer-Verlag, Berlin, 1983; Nauka, Moscow, 1989).

    MATH  Google Scholar 

  6. A. K. Gushchin, Dokl. Math. 72, 665–668 (2005) [Dokl. Akad. Nauk 404, 14–17 (2005)].

    Google Scholar 

  7. A. K. Gushchin, Sib. Mat. Zh. 46, 1036–1052 (2005).

    MATH  Google Scholar 

  8. A. K. Gushchin and V. P. Mikhailov, Mat. Sb. 185(1), 121–160 (1994).

    Google Scholar 

  9. L. Carleson, Am. J. Math. 80, 921–930 (1958).

    Article  MATH  Google Scholar 

  10. L. Hormander, Math. Scand. 20, 65–78 (1967).

    Google Scholar 

  11. A. K. Gushchin, Mat. Sb. 137, 19–64 (1988).

    Google Scholar 

  12. A. K. Gushchin and V. P. Mikhailov, Mat. Sb. 182, 787–810 (1991).

    Google Scholar 

  13. A. K. Gushchin, Mat. Sb. 189(7), 53–90 (1998).

    Google Scholar 

  14. A. K. Gushchin, Mat. Sb. 193(5), 17–36 (2002).

    Google Scholar 

  15. A. K. Gushchin, Dokl. Math. 69, 329–331 (2004) [Dokl. Akad. Nauk 396, 15–18 (2004)].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A.K. Gushchin, 2007, published in Doklady Akademii Nauk, 2007, Vol. 415, No. 1, pp. 10–13.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gushchin, A.K. Smoothness of solutions to the Dirichlet problem for a second-order elliptic equation with a square integrable boundary function. Dokl. Math. 76, 486–489 (2007). https://doi.org/10.1134/S1064562407040023

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562407040023

Keywords

Navigation