Skip to main content
SpringerLink
Log in

Comparison of Green Kernels for Elliptic Operators on (0,∞)

  • Published:
Potential Analysis Aims and scope Submit manuscript

Abstract

In this paper we give necessary and sufficient conditions for the comparability of Green kernels for second-order elliptic operators in the one-dimensional case.

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. Ancona, A.: ‘Comparaison des mesures harmoniques et des fonctions de Green pour des opérateurs elliptiques dans un domaine lipschitzien’, C. R. Acad. Sci. Paris 294 (1982), 505–508.

    Google Scholar 

  2. Cranston, M. and Zhao, Z.: ‘Conditional transformation of drift formula and potential theory for \(\frac{1}{2}\Delta+b(\cdot)\nabla\) ’, Comm. Math. Phys. 112 (1987), 613–625.

    Google Scholar 

  3. Cranston, M., Fabes, E.B. and Zhao, Z.: ‘Conditional gauge and potential theory for Schrödinger operator’, Trans. Amer. Math. Soc. 307 (1988).

  4. Hirsch, F.: ‘Conditions nécessaires et suffisantes d’existence de résolvantes’, Z. Wahr. Verw. Gebiete 29 (1974), 73–85.

    Google Scholar 

  5. Hueber, H. and Sieveking, M.: ‘Uniform bounds for quotients of Green functions on C1,1 domains’, Ann. Inst. Fourier 32(1) (1982), 105–117.

    Google Scholar 

  6. Maagli, H. and Syrine, M.: ‘Sur les solutions d’un opérateur differentiel singulier semi-lineaire’, Potential Anal. 10(3) (1999), 289–303.

    Google Scholar 

  7. Riahi, L.: ‘Comparison of Green functions for generalized Schrödinger operators on C1,1 domains’, J. Ineq. Pures Appl. Math. 4(1) (2003).

  8. Selmi, M.: ‘Critère de comparaison de certains noyaux de Green’, in Séminaire de Theorie du Potentiel, Lecture Notes in Math. 1235, 1987, pp. 172–193.

  9. Selmi, M.: ‘Comparaison des noyaux de Green sur les domaines C1,1’, Rev. Roumaine Math. Pures Appl. 36 (1991), 91–100.

    Google Scholar 

  10. Trimeche, K.: ‘Transformation intégrale de Weyl et théorème de Paley–Wiener associés a un opérateur différentiel singulier sur (0,∞)’, J. Math. Pures Appl. 60 (1981), 51–98.

    Google Scholar 

  11. Widder, D.V.: The Laplace Transform, Princeton Mathematical Series, 1946.

  12. Zhao, Z.: ‘Green function for Schrödinger operator and conditioned Feynman–Kac gauge’, J. Math. Anal. Appl. 116 (1986), 309–334.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis-Campus Universitaire, 1060, Tunis, Tunisia

    A. Ifra & M. Selmi

Authors
  1. A. Ifra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Selmi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Mathematics Subject Classifications (2000)

34B27, 34B05.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ifra, A., Selmi, M. Comparison of Green Kernels for Elliptic Operators on (0,∞). Potential Anal 23, 207–224 (2005). https://doi.org/10.1007/s11118-004-3262-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11118-004-3262-y

Keywords

Search

Navigation