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Remarks on the point interaction approximation

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1362)

Keywords

  • Diffusion Equation
  • Continuum Limit
  • Continuum Approximation
  • Spherical Inclusion
  • Sphere Center

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References for the Point Interaction Section

  1. E. I. Khruslov and V. A. Marchenko, Boundary value problems in regions with fine-grained boundaries, Naukova Dumka, Kiev, 1974.

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

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

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  4. G. Papanicolaou and S.R.S. Varadhan, Diffusion in regions with many small holes. In Stochastic Differential Systems (ed. B. Grigeliouis). Lecture Notes in Control and Information Theory 25, 190–206, Springer.

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  5. S. Ozawa, On an elaboration of M. Kac's Theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles, Comm. Math. Phys. 91, 1983, 473–487.

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  6. R. Figari, E. Orlandi and J. Teta, The Laplacian in regions with many small obstacles: fluctuations around the limit operator 41, 1985, 465–488.

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  7. L. L. Foldy, The multiple scattering of waves, Phys. Rev. 67, 1945, 107–119.

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  8. R. Caflisch, M. Miksis, G. Papanicolaou and L. Ting, Effective equations for wave propagation in bubbly liquids, J. Fluid Mech. 153, 1985, 259–273 and also 160, 1–14.

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  9. J. Rubinstein, NYU Dissertation, 1985.

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© 1988 Springer-Verlag

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Diaconis, P., Elworthy, D., Föllmer, H., Nelson, E., Papanicolaou, G., Varadhan, S.R.S. (1988). Remarks on the point interaction approximation. In: Hennequin, PL. (eds) École d'Été de Probabilités de Saint-Flour XV–XVII, 1985–87. Lecture Notes in Mathematics, vol 1362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086182

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  • DOI: https://doi.org/10.1007/BFb0086182

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50549-5

  • Online ISBN: 978-3-540-46042-8

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