Skip to main content
SpringerLink
Log in

Boundary Estimate for the Gradient of a Solution to the Dirichlet Problem for (p,q)-Nonlinear Equations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

(p, q)-Nonlinear elliptic equations are considered, where p, q, p \( < \) q, characterize the growth with respect to the gradient of eigenvalues of the principle matrix. Under the condition \(2 \leqslant p < q, q - p < \frac{2}{{n^2 + n}}p\) an a priori estimate for the maximum of the modulus of the gradient of a solution to the Dirichlet problem is obtained. Bibliography: 8 titles.

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. O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations [in Russian], Moscow, Nauka (1973); English transl.: Linear and Quasilinear Elliptic Equations, New York, Academic Press (1968).

    Google Scholar 

  2. J. Serrin, “The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables,” Philos. Trans. R. Soc. London, Ser. A, 264 (1969), 413–496.

    Google Scholar 

  3. A. V. Ivanov, “On the Dirichlet problem for quasilinear nonuniformly elliptic equations of the second order” [in Russian], Tr. MIAN, 116 (1971), No. 7, 34–54.

    Google Scholar 

  4. A. V. Ivanov, “Local estimates for the maximum of modulus of the first order derivatives for solutions to quasilinear nonuniformly elliptic equations of divergence form” [in Russian], Zap. Nauchn. Semin. LOMI, 7 (1968), 87–125.

    Google Scholar 

  5. P. Marcellini, “Regularity and existence of solutions of elliptic equations with p,q-growth conditions,” J. Differ. Equations, 90 (1991), No. 1, 1–30.

    Google Scholar 

  6. M. Bildhauer, “Convex variational Problems with Linear, Nearly Linear and/or Anisotropic Growth Conditions”, Preprint, Saarland Univ., No. D66041, November 16, 2001.

  7. O. A. Ladyzhenskaya and N. N. Uraltseva, “Boundary Estimates for the Hölder Norms of the Derivatives of Solutions to Quasilinear Elliptic and Parabolic Equations of General Form” [in Russian], Preprint, LOMI, P-I-85, Leningrad, 1985.

    Google Scholar 

  8. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Berlin, Springer (1977).

    Google Scholar 

Download references

Authors
  1. I. V. Nezhinskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nezhinskaya, I.V. Boundary Estimate for the Gradient of a Solution to the Dirichlet Problem for (p,q)-Nonlinear Equations. Journal of Mathematical Sciences 120, 1145–1154 (2004). https://doi.org/10.1023/B:JOTH.0000014843.14646.2b

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOTH.0000014843.14646.2b

Keywords

Search

Navigation