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On some elliptic transmission problems

Christodoulos Athanasiadis; Ioannis G. Stratis

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 2, page 137-154
  • ISSN: 0066-2216

Abstract

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Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of ℝ N . The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically different materials, is also studied.

How to cite

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Christodoulos Athanasiadis, and Ioannis G. Stratis. "On some elliptic transmission problems." Annales Polonici Mathematici 63.2 (1996): 137-154. <http://eudml.org/doc/262580>.

@article{ChristodoulosAthanasiadis1996,
abstract = {Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of $ℝ^N$. The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically different materials, is also studied.},
author = {Christodoulos Athanasiadis, Ioannis G. Stratis},
journal = {Annales Polonici Mathematici},
keywords = {transmission condition; Dirichlet problem; Robin problem; diffraction problem; acoustic scattering; existence; uniqueness; regularity results; transmission problem; infinitely stratified scatterer},
language = {eng},
number = {2},
pages = {137-154},
title = {On some elliptic transmission problems},
url = {http://eudml.org/doc/262580},
volume = {63},
year = {1996},
}

TY - JOUR
AU - Christodoulos Athanasiadis
AU - Ioannis G. Stratis
TI - On some elliptic transmission problems
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 2
SP - 137
EP - 154
AB - Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of $ℝ^N$. The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically different materials, is also studied.
LA - eng
KW - transmission condition; Dirichlet problem; Robin problem; diffraction problem; acoustic scattering; existence; uniqueness; regularity results; transmission problem; infinitely stratified scatterer
UR - http://eudml.org/doc/262580
ER -

References

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  2. [2] G. Dassios, Low frequency scattering theory for a penetrable body with an impenetrable core, SIAM J. Appl. Math. 42 (1982), 272-280. Zbl0488.35020
  3. [3] R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Physical Origins and Classical Methods, Springer, Berlin, 1990. Zbl0683.35001
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  9. [9] D. S. Jones, Acoustic and Electromagnetic Scattering, Clarendon Press, Oxford, 1986. 
  10. [10] R. E. Kleinman and G. F. Roach, Boundary integral equations for the three-dimensional Helmholtz equation, SIAM Rev. 16 (1974), 214-236. Zbl0253.35023
  11. [11] R. Kress and G. F. Roach, Transmission problems for the Helmholtz equation, J. Math. Phys. 19 (1978), 1433-1437. Zbl0433.35017
  12. [12] M. Krzyżański, Partial Differential Equations of Second Order, Vol. 1, PWN - Polish Scientific Publishers, Warszawa, 1971. Zbl0209.40003
  13. [13] O. A. Ladyzhenskaya, On the solution of the general diffraction problem, Dokl. Akad. Nauk SSSR 116 (1954), 433-436 (in Russian). 
  14. [14] O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Springer, New York, 1985. Zbl0588.35003
  15. [15] O. A. Oleĭnik, Boundary value problems for linear elliptic and parabolic equations with discontinuous coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 3-20 (in Russian). 
  16. [16] G. Stampacchia, Equations Elliptiques du Second Ordre à Coefficients Discontinus, Les Presses de l'Université de Montréal, 1966. Zbl0151.15501

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