Geodesic
On the Discrete Spectrum of Robin Laplacians in Conical Domains
K. Pankrashkin1
1 Laboratoire de mathématiques (UMR 8628 du CNRS), Université Paris-Sud Bâtiment 425, 91405 Orsay Cedex, France
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 100-110.

Voir la notice de l'article provenant de la source EDP Sciences

We discuss several geometric conditions guaranteeing the finiteness or the infiniteness of the discrete spectrum for Robin Laplacians in conical domains.
DOI : 10.1051/mmnp/201611208

K. Pankrashkin 1

1 Laboratoire de mathématiques (UMR 8628 du CNRS), Université Paris-Sud Bâtiment 425, 91405 Orsay Cedex, France 
@article{MMNP_2016_11_2_a7,
     author = {K. Pankrashkin},
     title = {On the {Discrete} {Spectrum} of {Robin} {Laplacians} in {Conical} {Domains}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {100--110},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2016},
     doi = {10.1051/mmnp/201611208},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611208/}
}
TY  - JOUR
AU  - K. Pankrashkin
TI  - On the Discrete Spectrum of Robin Laplacians in Conical Domains
JO  - Mathematical modelling of natural phenomena
PY  - 2016
SP  - 100
EP  - 110
VL  - 11
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611208/
DO  - 10.1051/mmnp/201611208
LA  - en
ID  - MMNP_2016_11_2_a7
ER  - 
%0 Journal Article
%A K. Pankrashkin
%T On the Discrete Spectrum of Robin Laplacians in Conical Domains
%J Mathematical modelling of natural phenomena
%D 2016
%P 100-110
%V 11
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611208/
%R 10.1051/mmnp/201611208
%G en
%F MMNP_2016_11_2_a7
K. Pankrashkin. On the Discrete Spectrum of Robin Laplacians in Conical Domains. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 2, pp. 100-110. doi : 10.1051/mmnp/201611208. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611208/

[1] J. Behrndt, P. Exner, V. Lotoreichik J. Phys. A: Math. Theor 2014

[2] V. Bonnaillie-Noël, H. Kovařík, K. Pankrashkin (Eds): Mini-workshop: Eigenvalue problems in surface superconductivity. Oberwolfach Rep. (to appear).

[3] P. Bryan, J. Louie: Classification of convex ancient solutions to curve shortening flow on the sphere. J. Geom. Anal. (to appear). Preprint arXiv:1408.5523.

[4] D. Daners, J. B Kennedy: On the asymptotic behaviour of the eigenvalues of a Robin problem. Differ. Integr. Eq., 237/8 (2010), 659–669.

[5] M. Dauge, T. Ourmières-Bonafos, N. Raymond Commun. Pure Appl. Anal. 2015 1239 1258

[6] G. Del Grosso, M. Campanino: A construction of the stochastic process associated to heat diffusion in a polygonal domain. Bolletino Unione Mat. Ital., 13-B (1976) 876–895.

[7] P. Exner, A. Minakov J. Math. Phys. 2014 122101

[8] P. Exner, A. Minakov, L. Parnovski Portugal. Math. 2014 141 156

[9] P. Exner, M. Tater J. Phys. A: Math. Theor. 2010

[10] T. Giorgi, R. Smits Z. Angew. Math. Phys. 2007 224 245

[11] B. Helffer, K. Pankrashkin J. London Math. Soc. 2015 225 248

[12] B. Helffer, A. Kachmar: Eigenvalues for the Robin Laplacian in domains with variable curvature. Tran. Amer. Math. Soc. (to appear), preprint arXiv:1411.2700 (2014).

[13] P. D. Hislop, I. M. Sigal: Introduction to spectral theory. Springer, 1995.

[14] A. A. Lacey, J. R. Ockendon, J. Sabina SIAM J. Appl. Math. 1998 1622 1647

[15] M. Levitin, L. Parnovski Math. Nachr. 2008 272 281

[16] Y. Lou, M. Zhu Pacific J. Math. 2004 323 334

[17] K. Pankrashkin Nanosystems: Phys. Chem. Math. 2013 474 483

[18] K. Pankrashkin Nanosystems: Phys. Chem. Math. 2015 46 56

[19] K. Pankrashkin, N. Popoff: Mean curvature bounds and eigenvalues of Robin Laplacians. Calc. Var. PDE. (to appear), preprint arXiv:1407.3087 (2014).

[20] K. Pankrashkin, N. Popoff: An effective Hamiltonian for the eigenvalue asymptotics of a Robin Laplacian with a large parameter. Preprint arXiv:1502.00877 (2015).

Cité par Sources :