Skip to main content
Log in

Unimprovable estimates for solutions of a mixed problem for linear elliptic equations of the second order in a neighborhood of an angular point

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Under the minimal conditions for the smoothness of the coefficients of an equation, unimprovable estimates are obtained for solutions of a mixed problem for linear nondivergent elliptic equations of the second order in a neighborhood of an angular point of the boundary of a domain.

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.

Similar content being viewed by others

References

  1. A. Azzam, “Smoothness properties of solutions of mixed boundary-value problems for elliptic equations in sectionally smooth n-dimensional domains,” Ann. Polon. Math., 40, 81–93 (1981).

    MATH  MathSciNet  Google Scholar 

  2. A. Azzam and E. Kreyszig, “Über das gesmischte Randwertproblem for ellische Gleichunden in n-dimensionalen Gebieten mit Kanten.” Ann. Acad. Sci. Fenn. Ser. Al Math., 5, 431–436 (1981).

    Google Scholar 

  3. A. Azzam and E. Kreyszig, “On solution of elliptic equations satisfying mixed boundary conditions,” SIAM J. Math. Anal., 13, 254–262 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Grisvard, Elliptic Problem in Nonsmooth Domains, Pitman, Boston (1985).

    Google Scholar 

  5. G. M. Lieberman, “Mixed boundary value problems for elliptic and parabolic differential equations of second order,” J. Math. Anal. Appl., 113, 422–440 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  6. G.M. Lieberman, “Optimal Hölder regularity for mixed boundary-value problem,” J. Math. Anal. Appl., 113, 572–586 (1989).

    Article  MathSciNet  Google Scholar 

  7. M. V. Borsuk, First Boundary-Value Problem for Elliptic Equations of the Second Order in Domains with Conical and Angular Points on the Boundary [in Russian], Author’s Abstract of the Doctoral-Degree Thesis (Physics and Mathematics), Lviv (1993).

    Google Scholar 

  8. M. V. Borsuk, “Unimprovable estimates for the Dirichlet problem for linear elliptic nondivergent equations of the second order in the neighborhood of a conical point of the boundary,” Mat. Sb., 182, No. 10, 1446–1462 (1991).

    MATH  Google Scholar 

  9. S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the Boundary for Solution of Elliptic Partial Difference Equations Satisfying General Boundary Conditions., Interscience, New York (1959).

    Google Scholar 

Download references

Authors

Additional information

Lviv University, Lviv. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 11, pp. 1529–1542, November, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chernets’kyi, V.Z. Unimprovable estimates for solutions of a mixed problem for linear elliptic equations of the second order in a neighborhood of an angular point. Ukr Math J 49, 1718–1734 (1997). https://doi.org/10.1007/BF02487510

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487510

Keywords

Navigation