Propriétés spectrales des valeurs propres intérieures de transmission
Luc Robbiano1
1 Laboratoire de Mathématiques de Versailles Université de Versailles St Quentin & CNRS UMR 8100 45, Avenue des États-Unis 78035 Versailles France
Séminaire Laurent Schwartz — EDP et applications (2013-2014), Talk no. 17, 9 p.

Nous présentons ici quelques résultats concernant les valeurs propres intérieures de transmission et nous donnons, sous certaines hypothèses une asymptotique de la fonction de comptage de Weyl.

DOI: 10.5802/slsedp.61
Luc Robbiano 1

1 Laboratoire de Mathématiques de Versailles Université de Versailles St Quentin & CNRS UMR 8100 45, Avenue des États-Unis 78035 Versailles France 
@article{SLSEDP_2013-2014____A17_0,
     author = {Luc Robbiano},
     title = {Propri\'et\'es spectrales des valeurs propres int\'erieures de~transmission},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:17},
     pages = {1--9},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2013-2014},
     doi = {10.5802/slsedp.61},
     language = {fr},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.61/}
}
TY  - JOUR
AU  - Luc Robbiano
TI  - Propriétés spectrales des valeurs propres intérieures de transmission
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:17
PY  - 2013-2014
SP  - 1
EP  - 9
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.61/
DO  - 10.5802/slsedp.61
LA  - fr
ID  - SLSEDP_2013-2014____A17_0
ER  - 
%0 Journal Article
%A Luc Robbiano
%T Propriétés spectrales des valeurs propres intérieures de transmission
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:17
%D 2013-2014
%P 1-9
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.61/
%R 10.5802/slsedp.61
%G fr
%F SLSEDP_2013-2014____A17_0
Luc Robbiano. Propriétés spectrales des valeurs propres intérieures de transmission. Séminaire Laurent Schwartz — EDP et applications (2013-2014), Talk no. 17, 9 p. doi : 10.5802/slsedp.61. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.61/

[1] Agmon Shmuel, Lectures on elliptic boundary value problems. Van Nostrand Mathematical Studies, No. 2, 1965. | MR | Zbl

[2] Cakoni Fioralba, Çayören Mehmet, Colton David, Transmission eigenvalues and the nondestructive testing of dielectrics. Inverse Problems 24 (2008) 065016. | MR | Zbl

[3] Cakoni Fioralba, Colton David, Haddar Houssem, The interior transmission problem for regions with cavities. SIAM J. Math. Anal. 42 (2010) 145–162. | MR | Zbl

[4] Cakoni Fioralba, Gintides Drossos, Haddar Houssem, The existence of an infinite discrete set of transmission eigenvalues. SIAM J. Math. Anal. 42 (2010) 237–255. | MR | Zbl

[5] Cakoni Fioralba, Haddar Houssem, Transmission Eigenvalues in Inverse Scattering Theory. | HAL

[6] Colton David, Kirsch Andreas, Päivärinta Lassi, Far-field patterns for acoustic waves in an inhomogeneous medium. SIAM J. Math. Anal. 20 (1989) 1472–1483. | MR | Zbl

[7] Colton David, Kress Rainer, Inverse acoustic and electromagnetic scattering theory. Applied Mathematical Sciences, 93, Springer-Verlag, Berlin, 1992. | MR | Zbl

[8] Dimassi Mouez , Petkov Vesselin, Upper bound for the counting function of interior transmission eigenvalues, . | arXiv

[9] Faierman Melvin, Transmission eigenvalues for parameter-elliptic boundary problems, preprint.

[10] Hitrik Michael, Krupchyk Katsiaryna, Ola Petri, Päivärinta Lassi. Transmission eigenvalues for operators with constant coefficients. SIAM J. Math. Anal. 42 (2010) 2965–2986. | MR | Zbl

[11] Hitrik Michael, Krupchyk Katsiaryna, Ola Petri, Päivärinta Lassi, Transmission eigenvalues for elliptic operators. SIAM J. Math. Anal. 43 (2011) 2630–2639. | MR | Zbl

[12] Hitrik Michael, Krupchyk Katsiaryna, Ola Petri, Päivärinta Lassi, The interior transmission problem and bounds on transmission eigenvalues, . | arXiv | Zbl

[13] Karamata, J., Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze. Math. Z. 33 (1931) 294–299. | MR | Zbl

[14] Lakshtanov Evgeny, Vainberg Boris, Ellipticity in the Interior Transmission Problem in Anisotropic Media. SIAM J. Math. Anal. 44 (2012) 1165–1174. | MR | Zbl

[15] Lakshtanov Evgeny, Vainberg Boris, Remarks on interior transmission eigenvalues, Weyl formula and branching billiards. J. Phys. A : Math. Theor 45 125202. | MR | Zbl

[16] Lakshtanov Evgeny, Vainberg Boris, Bounds on positive interior transmission eigenvalues. | arXiv | MR

[17] Lakshtanov Evgeny, Vainberg Boris, Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem. | arXiv | MR | Zbl

[18] Lakshtanov Evgeny, Vainberg Boris, Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues. | arXiv

[19] Malliavin, Paul, Un théorème taubérien relié aux estimations de valeurs propres. Séminaire Jean Leray (1962-1963) 224–231 numdam.

[20] Päivärinta Lassi, Sylvester John, Transmission eigenvalues. SIAM J. Math. Anal. 40 (2008) 738–753. | MR | Zbl

[21] Petkov Vesselin, Vodev Georgi Asymptotics of the number of the interior transmission eigenvalues. | arXiv

[22] Pham Ha, Stefanov Plamen, Weyl asymptotics of the transmission eigenvalues for a constant index of refraction. | arXiv

[23] Robbiano Luc, Spectral analysis on interior transmission eigenvalues. Inverse Problems 29 (2013) 104001 | MR

[24] Robbiano Luc, Counting function for interior transmission eigenvalues. | HAL

[25] Sylvester John, Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators. SIAM J. Math. Anal. 44 (2012) 341–354. | MR | Zbl

Cited by Sources: