Skip to main content
SpringerLink
Log in

L p -Regularity for the Cauchy-Dirichlet Problem for Parabolic Equations in Convex Polyhedral Domains

  • Published:
Acta Mathematica Vietnamica Aims and scope Submit manuscript

Abstract

In this paper, we study the regularity of the solution of the initial-boundary value problem with Dirichlet boundary conditions for second-order divergence parabolic equations in a domain of polyhedral type. We establish several results on the regularity of the solution in weighted L p -Sobolev spaces.

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. Alkhutov, A.Y., Gordeev, A.N.: L p -estimates for solutions to second order parabolic equations. In: Proceedings of the St. Petersburg Mathematical Society. Am. Math. Soc. Transl. Ser. 2 222. Am. Math. Soc., Providence, RI, vol. 13, pp 1–21 (2008)

  2. Bramanti, M., Cerutti, M.C.: \(W_p^{1,2}\) solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients. Comm. Partial Differ. Equations 18(9–10), 1735–1763 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Byun, S.S.: Parabolic equations with BMO coefficients in Lipschitz domains. J. Differ. Equations 209, 229–265 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hung, N.M., Anh, N.T.: Regularity of solutions of initial–boundary value problems for parabolic equations in domains with conical points. J. Differ. Equations 245, 1801–1818 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kozlov, V.A., Maz’ya, V.G., Rossman, J.: Spectral problems associated with corner singularities of solutions to elliptic equation. Mathematical Surveys and Monographs, 85. Am. Math. Soc., Providence, RI (2001)

  6. Maz’ya, V.G., Rossmann, J.: Elliptic Equations in Polyhedral Domains. Mathematical Surveys and Monographs, 162. Am. Math. Soc., Providence, Rhode Island (2010)

  7. Ladyzhenskaya, O.A., Solonnikov, V.A., Uraltseva, N.N.: Linear and Quasilinear Equations of Parabolic type. Moscow, Nauka (1967)

    Google Scholar 

  8. Solonnikov, V.A.: L p -estimates for solutions of the heat equation in a dihedral angle. Rend. Mat. Appl., Serie VII 21, 1–15 (2001)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tay Bac University, Sonla, Vietnam

    Vu Trong Luong

  2. Vietnam Education Publishing House, Hanoi, Vietnam

    Nguyen Thanh Anh

  3. Department of Mathematics, Hong Duc University, Thanhhoa, Vietnam

    Do Van Loi

Authors
  1. Vu Trong Luong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nguyen Thanh Anh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Do Van Loi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vu Trong Luong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luong, V.T., Anh, N.T. & Van Loi, D. L p -Regularity for the Cauchy-Dirichlet Problem for Parabolic Equations in Convex Polyhedral Domains. Acta Math Vietnam 41, 731–742 (2016). https://doi.org/10.1007/s40306-016-0172-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40306-016-0172-1

Keywords

Mathematical Subject Classification (2010)

Search

Navigation