Weyl Type Bound on Positive Interior Transmission Eigenvalues

Communications in Partial Differential Equations

Volumn 39, Issue 9, 2014, Pages 1729-1740

  Lakshtanov, E ^a   Vainberg, B ^b  

^a UNIVERSITY OF AVEIRO   (Portugal)

^b UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Counting function; Interior transmission eigenvalues; Weyl formula

Indexed keywords

EID: 84905660318     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605302.2014.881853     Document Type: Article

References (18)

1. Bonnet-BenDhia, A.-S., Chesnel, L., Haddar, H. (2011). On the use of T-coercivity to study the interior transmission eigenvalue problem. Comptes Rendus Mathematique 349:647-651.
2. Cakoni, F., Cossonniere, A., Haddar, H. (2012). Transmission eigenvalues for inhomogeneous media containing obstacles. Inverse problems and Imaging 6: 373 - 398.
3. Cakoni, F., Gintides, D., Haddar, H. (2010). The existence of an infinite discrete set of transmission eigenvalues. SIAM J. Math. Anal. 42: 237 - 255.
4. Cakoni, F., Haddar, H. (2012). Transmission eigenvalues in inverse scattering theory. Inside Out II MSRI Publications 60: 529 - 580.
5. Cakoni, F., Kirsch, A. (2010). On the interior transmission eigenvalue problem. Int. Jour. Comp. Sci. Math. 3: 142 - 167.
6. Friedlander, L. (1991). Some inequalities between Dirichlet and Neumann eigenvalues. Archive for Rational Mechanics and Analysis 116: 153 - 160.
7. Hitrik, M., Krupchyk, K., Ola, P., Paivarinta, L. (2011). The interior transmission problem and bounds on transmission eigenvalues. Math. Res. Lett. 18: 279 - 293.
8. Hitrik, M., Krupchyk, K., Ola, P., Paivarinta, L. (2011). Transmission eigenvalues for elliptic operators. SIAM J. Math. Anal. 43: 2630 - 2639.
9. Lakshtanov, E., Vainberg, B. (2012). Bounds on positive interior transmission eigenvalues. Inverse Problems 28: 105005.
10. Lakshtanov, E., Vainberg, B. (2012). Ellipticity in the interior transmission problem in anisotropic media. SIAM J. Math. Anal. 44: 1165 - 1174.
11. Lakshtanov, E., Vainberg, B. (2012). Remarks on interior transmission eigenvalues, Weyl formula and branching billiards. J. Phys. A: Math. Theor. 45: 125 - 202.
12. Lakshtanov, E., Vainberg, B. (2013). Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem. Inverse Problems 29: 104003.
13. Reed, M., Simon, B. (1978). Methods of Modern Mathematical Physics IV. New York: Academic Press.
14. Robbiano, L. (2013). Spectral analysis on interior transmission eigenvalues. Inverse Problems 29: 1044001.
15. Roitberg, Y. (1996). Elliptic Boundary Value Problems in the Spaces of Distributions. Vol. 384. Dordrecht, the Netherlands: Kluwer Academic Pub.
16. Safarov, Y., Vassiliev, D. (1997/1998).
17. Serov, V., Sylvester, J. (2012). Transmission Eigenvalues: Some degenerate and singular cases. Inverse Problems 28: 065004.
18. Sylvester, J. (2011). Discreteness of transmission eigenvalues via upper triangular compact operators. SIAM J. Math. Anal. 44: 341 - 354.