Skip to main content
SpringerLink
Log in

On a singular perturbation problem involving the distance to a curve

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

References

  1. N. André and I. Shafrir,Minimization of a Ginzburg-Landau type functional with nonvanishing Dirichlet boundary condition, Calc. Var. Partial Differential Equations7 (1998), 191–217.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. André and I. Shafrir,On nematics stabilized by a large external field, Rev. Math. Phys.11 (1999), 653–710.

    Article  MATH  MathSciNet  Google Scholar 

  3. N. André and I. Shafrir,On the minimizers of a Ginzburg-Landau energy when the boundary condition has zeros, preprint.

  4. S. B. Angenent,Uniqueness of the solution of a semilinear boundary value problem, Math. Ann.272 (1985), 129–138.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. S. Berger and L. E. Fraenkel,On the asymptotic solution of a nonlinear Dirichlet problem, J. Math. Mech.19 (1970), 553–585.

    MATH  MathSciNet  Google Scholar 

  6. F. Bethuel, H. Brezis and F. Hélein,Asymptotics for the minimizers of a Ginzburg-Landau functional, Calc. Var. Partial Differential Equations1 (1993), 123–148.

    Article  MATH  MathSciNet  Google Scholar 

  7. F. Bethuel, H. Brezis and F. Hélein,Ginzburg-Landau Vortices, BirkhÄuser, Basel, 1994.

    MATH  Google Scholar 

  8. F. Bethuel and T. Rivière,Vortices for a variational problem related to superconductivity, Ann. Inst. H. Poicaré Anal. Non Linéaire12 (1995), 243–303.

    MATH  Google Scholar 

  9. H. Brezis, F. Merle and T. Rivière,Quantization effects for -δu = u(l-u2)in ℝ2, Arch. Rational Mech. Anal.126 (1994), 35–58.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Chipot, M. Chlebík, M. Fila and I. Shafrir,Existence of positive solutions of a semilinear elliptic equation in ℝ n+ with a nonlinear boundary condition, J. Math. Anal. Appl.223 (1998), 429–471.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. I. Choi, S. W. Choi and H. P. Moon,Mathematical theory of Medial axis transform, Pacific J. Math.181(1997), 57–88.

    Article  MathSciNet  Google Scholar 

  12. D. Gilbarg and N. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin and New York, 1983.

    MATH  Google Scholar 

  13. L. Lassoued and P. Mironescu,Ginzburg-Landau type energy with discontinuous constraint, J. Analyse Math.77 (1999), 1–26.

    Article  MATH  MathSciNet  Google Scholar 

  14. L. Modica,The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal.98 (1987), 123–142.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Serrin,Nonlinear elliptic equations of second order, AMS Symposium in Partial Differential Equations, Berkeley, 1971.

    Google Scholar 

  16. M. Struwe,On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions, Differential Integral Equations7 (1994), 1613–1624;erratum, loc. cit.8 (1995), 124.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Université de Tours, 37200, Tours, France

    N. André

  2. Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    I. Shafrir

Authors
  1. N. André
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Shafrir
    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

André, N., Shafrir, I. On a singular perturbation problem involving the distance to a curve. J. Anal. Math. 90, 337–396 (2003). https://doi.org/10.1007/BF02786561

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02786561

Keywords

Search

Navigation