Skip to main content
SpringerLink
Log in

Divergence-free Hardy space on ℝN +

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

We introduce a divergence-free Hardy space H 1 z,div (ℝN +, ℝN) and prove its divergencefree atomic decomposition. We also characterize its dual space and establish a “div-curl” type theorem on ℝ3 + with an application to coercivity properties of some polyconvex quadratic forms.

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. Gilbert, J. E., Hogan, J. A., Lakey, J. D., Atomic decomposition of divergence-free Hardy spaces, Mathematica Moraviza, 1997, Special Volume, Proc. IWAA: 33–52.

  2. Chang, D. C., Krantz, S. G., Stein, E. M., Hp theory on a smooth domain in RN and elliptic boundary value problems, J. Funct. Anal., 1993, 114: 286–347.

    Article  MathSciNet  MATH  Google Scholar 

  3. Schwarz, G., Hodge Decomposition-A method for solving boundary value problems, Lecture Notes in Mathematics, Vol. 1607, Berlin Heidelberg: Springer-Verlag, 1995.

    Google Scholar 

  4. Girault, V., Raviart, P. A., Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Berlin Heidelberg: Springer-Verlag, 1986.

    Book  MATH  Google Scholar 

  5. Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton: Princeton Univ. Press, 1970.

    MATH  Google Scholar 

  6. Davies, B., Heat Kernels and Spectral Theory, Cambridge: Cambridge University Press, 1989.

    Book  MATH  Google Scholar 

  7. Geymonat, G., Müller, S., Triantafylidis, N., Homogenization of nonlinear elastic materials, microscopic bifurcation and microscopic loss of rank-one convexity, Arch. Rational Mech. Anal., 1993, 122: 231–290.

    Article  MathSciNet  MATH  Google Scholar 

  8. Ball, J., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 1977, 63: 337–403.

    Article  MATH  Google Scholar 

  9. Zhang, K., On the coercivity of elliptic systems in two dimensional spaces, Bull. Austral. Math. Soc., 1996, 54: 423–430.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Shantou University, 515063, Shantou, China

    Zengjian Lou

  2. Center for Mathematics and Its Applications, Mathematical Science Institute, Australian National University, 0200, Canberra, ACT, Australia

    McIntosh Alan

Authors
  1. Zengjian Lou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. McIntosh Alan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Zengjian Lou or McIntosh Alan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zengjian, L., McIntosh, A. Divergence-free Hardy space on ℝN + . Sci. China Ser. A-Math. 47, 198–208 (2004). https://doi.org/10.1360/02ys0363

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1360/02ys0363

Keywords

Search

Navigation