Skip to main content

Approximation of Green's function in a region with many obstacles

Part of the Lecture Notes in Mathematics book series (LNM,volume 1339)

Keywords

  • Grained Boundary
  • Random Medium
  • Dirichlet Condition
  • Interact Particle System
  • Schrodinger Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. I. Chavel and E. A. Feldman, The Wiener sausage and a theorem of Spitzer in Riemannian manifolds, Probability and harmonic analysis, J. Chao and W. A. Woyczynski, eds., Marcel Dekker Inc., (1986), 45–60.

    Google Scholar 

  2. W. Feller, An introduction to probability theory and its applications, II, John Wiley and Sons, Inc., 1966.

    Google Scholar 

  3. E. Ja. Huruslov and V. A. Marchenko, Boundary value problems in regions with fine grained boundaries. (in Russian) Kiev 1974.

    Google Scholar 

  4. R. Figari, E. Orlandi and S. Teta, The Laplacian in regions with many obstacles: Fluctuations around the limit operator, J. Statistical Phys., 41 (1985), 465–487.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M. Kac, Probabilistic methods in some problems of scattering theory, Rocky Mountain J. Math., 4 (1974), 511–538.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. S. Ozawa, Random media and eigenvalues of the Laplacian, Commun. Math. Phys., 94 (1984), 421–437.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. _____, Point interaction approximation for (−Δ+U)−1 and eigenvalues of the Laplacian on wildly perturbed domain, Osaka J. Math. 20 (1983), 923–937.

    MathSciNet  MATH  Google Scholar 

  8. _____, Fluctuation of spectra in random media, Proceedings of the Taniguchi symposium "Probabilistic methods in mathematical physics" eds., by N. Ikeda and K. Ito, Kinokuniya, (1987), 335–361.

    Google Scholar 

  9. _____, Construction of approximate eigenfunction in disordered media. in prep.

    Google Scholar 

  10. _____, Mathematical study of spectra in random media, in Hydrodynamic behaviour and infinite interacting particle system, IMA series in mathematics, Springer 1987.

    Google Scholar 

  11. J. Rauch and M. Taylor, Potential and scattering theory on wildly perturbed domains, J. Funct. Anal. 18 (1975), 27–59.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. A. S. Sznitman, Some bounds and limiting results for the measure of Wiener sausage of small radius associated to elliptic diffusions, Stochastic processes and their applications., 25, (1987), 1–25.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. S. Weinryb, Etude asymptotique de l'image par des measures de certains ensembles aleatoires liés à la courbe Brownienne, Prob. Theory Rel. Fields 73 (1986), 135–148.

    CrossRef  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Ozawa, S. (1988). Approximation of Green's function in a region with many obstacles. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083057

Download citation

  • DOI: https://doi.org/10.1007/BFb0083057

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50113-8

  • Online ISBN: 978-3-540-45930-9

  • eBook Packages: Springer Book Archive