Communications in Mathematical Physics

, Volume 163, Issue 2, pp 395–414 | Cite as

P-determinant regularization method for elliptic boundary problems

  • Oscar A. Barraza
Article

Abstract

An expression for thep-determinant of the quotient of two differential elliptic operators with boundary conditions is given in terms of the boundary values of their solutions. Applications to physical examples are considered.

Keywords

Boundary Condition Neural Network Statistical Physic Complex System Nonlinear Dynamics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barraza, O., Falomir, H., Gamboa Saraví, R.E., Santangelo, E.M.:P-determinants and boundary values. J. Math. Phys.33, 6 (1992)Google Scholar
  2. 2.
    Calderón, A. P.: Pseudodifferential operators and elliptic boundary value problems I. Publicaciones del I.A.M., núm. 1, Buenos Aires 1976Google Scholar
  3. 3.
    De Francia, M., Falomir, H., Santangelo, E.M.: Free energy of a four-dimensional chiral bag. Phys. Rev. D45, 6 (1992)Google Scholar
  4. 4.
    Dunford, N., Schwartz, J.: Linear operators. II. New York: Interscience 1958Google Scholar
  5. 5.
    Forman, R.: Functional determinants and geometry. Invent. Math.88, 447–493 (1987)Google Scholar
  6. 6.
    Gohberg, I.C., Krein, M.G.: Introduction to the theory of linear nonselfadjoint operators, vol. 18 (Translation of Mathematical Monographs). Providence, R.I.: American Mathematical Society 1969Google Scholar
  7. 7.
    Hörmander, L.: The analysis of the linear partial differential operators. III. Berlin, Heidelberg, New York: Springer 1985Google Scholar
  8. 8.
    Seeley, R.: The resolvent of an elliptic boundary problem. Am. J. Math.91, 889–920 (1969)Google Scholar
  9. 9.
    Simon, B.: Trace ideals and their applications. London Mathematical Society, Lecture Notes Series 35. Cambridge: Cambridge University Press 1979Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Oscar A. Barraza
    • 1
    • 2
  1. 1.Departamento de MatemáticaU.N.L.P.La PlataArgentina
  2. 2.Universidad de San AndrésBuenos AiresArgentina

Personalised recommendations