# On some elliptic transmission problems

Christodoulos Athanasiadis; Ioannis G. Stratis

Annales Polonici Mathematici (1996)

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

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topChristodoulos 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

top- [1] D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Wiley, New York, 1983. Zbl0522.35001
- [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] 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
- [4] R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 4, Integral Equations and Numerical Methods, Springer, Berlin, 1990. Zbl0784.73001
- [5] D. E. Edmunds and W. D. Evans, Elliptic and degenerate-elliptic operators in unbounded domains, Ann. Scuola Norm. Sup. Pisa (3) 27 (1973), 591-640. Zbl0298.35027
- [6] G. Fichera, Existence theorems in elasticity, in: Handbuch der Physik, Springer, Berlin, VIa/2, 1972, 347-389.
- [7] P. R. Garabedian, Partial Differential Equations, Wiley, New York, 1964. Zbl0124.30501
- [8] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. Zbl0361.35003
- [9] D. S. Jones, Acoustic and Electromagnetic Scattering, Clarendon Press, Oxford, 1986.
- [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] R. Kress and G. F. Roach, Transmission problems for the Helmholtz equation, J. Math. Phys. 19 (1978), 1433-1437. Zbl0433.35017
- [12] M. Krzyżański, Partial Differential Equations of Second Order, Vol. 1, PWN - Polish Scientific Publishers, Warszawa, 1971. Zbl0209.40003
- [13] O. A. Ladyzhenskaya, On the solution of the general diffraction problem, Dokl. Akad. Nauk SSSR 116 (1954), 433-436 (in Russian).
- [14] O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Springer, New York, 1985. Zbl0588.35003
- [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] G. Stampacchia, Equations Elliptiques du Second Ordre à Coefficients Discontinus, Les Presses de l'Université de Montréal, 1966. Zbl0151.15501

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