Skip to main content
SpringerLink
Log in

Regularity of a boundary point for singular parabolic equations with measurable coefficients

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the continuity of solutions of quasilinear parabolic equations near the nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for the regularity of a boundary point, which coincides with the Wiener condition for the Laplace p-operator. The model case of the equations considered is the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the Laplace p-operator Δ p for 2n / (n + 1) < p < 2.

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

REFERENCES

  1. E. Di Benedetto, “On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients,” Ann. Sci. Norm. Supér Pisa Cl. Sci. Ser. IV, XIII, 487–535 (1986).

  2. E. Di Benedetto (1993) Degenerate Parabolic Equations Springer New York

    Google Scholar 

  3. A. N. Tikhonov (1938) ArticleTitleOn heat equations for several variables Byull. Mosk. Univ. Sektsiya A 1 IssueID9 1–49

    Google Scholar 

  4. N. Eklund (1971) ArticleTitleBoundary behavior of solutions of parabolic equations with discontinuous coefficients Bull.Amer. Math. Soc. 77 788–792

    Google Scholar 

  5. W. P. Ziemer (1980) ArticleTitleBehavior at the boundary of solutions of quasilinear parabolic equations J. Different. Equat. 35 IssueID3 291–305

    Google Scholar 

  6. I. V. Skrypnik (1992) ArticleTitleNecessary conditions for the regularity of a boundary point for a quasilinear parabolic equation Mat. Sb. 183 IssueID7 3–22

    Google Scholar 

  7. I. I. Skrypnik (2000) ArticleTitleRegularity of a boundary point for degenerate parabolic equations with measurable coefficients Ukr. Mat. Zh. 52 IssueID11 1550–1565

    Google Scholar 

  8. I. I. Skrypnik (2003) ArticleTitleNecessary condition for the regularity of a boundary point for degenerate parabolic equations with measurable coefficients Tr. Inst. Prikl. Mat. Mekh. NAN Ukr. 8 147–167

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    I. I. Skrypnik

Authors
  1. I. I. Skrypnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 506–516, April, 2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skrypnik, I.I. Regularity of a boundary point for singular parabolic equations with measurable coefficients. Ukr Math J 56, 614–627 (2004). https://doi.org/10.1007/s11253-005-0007-z

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-005-0007-z

Keywords

Search

Navigation