Skip to main content
SpringerLink
Log in

Global Higher Integrability of the Gradient of Weak Solutions of a Quasilinear Elliptic Equation

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we establish global higher integrability of the gradient of the solution of the quasilinear elliptic equation \(\Delta _A u=\text {div}\left( \frac{a(|F|)}{|F|}F\right) \) in \({\mathbb {R}}^n\), where \(\Delta _A\) is the so called A-Laplace operator.

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. Adams, R.A., Fournier, J.J.F.: Sobolev Spaces, 2nd edn. Academic Press, Berlin (2003)

    MATH  Google Scholar 

  2. Alessandrini, G., Sigalotti, M.: Geometric properties of solutions to the anisotropic p-Laplace equation in dimension two. Ann. Acad. Sci. Fenn. Math. 26(1), 249–266 (2001)

    MathSciNet  MATH  Google Scholar 

  3. Challal, S., Lyaghfouri, A.: Hölder continuity of solutions to the \(A\)-Laplace equation involving measures. Commun. Pure Appl. Anal. 8(5), 1577–1583 (2009)

    Article  MathSciNet  Google Scholar 

  4. Challal, S., Lyaghfouri, A., Rodrigues, J.F.: On the \(A\)-obstacle problem and the Hausdorff measure of its free boundary. Ann. Mat. 191, 113–165 (2012)

    Article  MathSciNet  Google Scholar 

  5. DiBenedetto, E., Manfredi, J.: On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Am. J. Math. 115(5), 1107–1134 (1993)

    Article  MathSciNet  Google Scholar 

  6. Fujii, N.: A proof of the Fefferman–Stein–Strömberg inequality for the sharp maximal functions. Proc. Am. Math. Soc. 106(2), 371–377 (1989)

    MATH  Google Scholar 

  7. Gallardo, D.: Orlicz spaces for which the Hardy–Littlewood maximal operator is bounded. Publ. Mat. 32, 261–266 (1988)

    Article  MathSciNet  Google Scholar 

  8. Iwaniec, T.: Projections onto gradient fields and \(L^P\)-estimates for degenerate elliptic equations. Stud. Math. 75, 293–312 (1983)

    Article  Google Scholar 

  9. Lieberman, G.M.: The natural generalization of the natural conditions of Ladyzhenskaya and Uraltseva for elliptic equations. Commun. Partial Differ. Equ. 16(2–3), 311–361 (1991)

    Article  MathSciNet  Google Scholar 

  10. Musielak, J.: Orlicz Spaces and Modular Spaces. Springer, Berlin (1983)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. United Arab Emirates University, Department of Mathematical Sciences, Al Ain, Abu Dhabi, UAE

    Abdeslem Lyaghfouri

Authors
  1. Abdeslem Lyaghfouri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdeslem Lyaghfouri.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lyaghfouri, A. Global Higher Integrability of the Gradient of Weak Solutions of a Quasilinear Elliptic Equation. Mediterr. J. Math. 19, 178 (2022). https://doi.org/10.1007/s00009-022-02095-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-022-02095-2

Keywords

Mathematics Subject Classification

Search

Navigation