no. 3
Une inégalité de Cheeger pour le spectre de Steklov
Jammes, Pierre1
1 Univ. Nice Sophia Antipolis CNRS, LJAD, UMR 7351 06100 Nice (France)
Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1381-1385.

On montre une inégalité de Cheeger pour la première valeur propre de Steklov. Elle fait intervenir deux constantes isopérimétriques.

We prove a Cheeger inequality for the first positive Steklov eigenvalue. It involves two isoperimetric constants.

DOI : 10.5802/aif.2960
Classification : 35P15, 58J50
Mot clés : inégalité de Cheeger, spectre de Steklov
Keywords: Cheeger inequality, Steklov eigenvalues.

Jammes, Pierre 1

1 Univ. Nice Sophia Antipolis CNRS, LJAD, UMR 7351 06100 Nice (France) 
@article{AIF_2015__65_3_1381_0,
     author = {Jammes, Pierre},
     title = {Une in\'egalit\'e de {Cheeger} pour le spectre de {Steklov}},
     journal = {Annales de l'Institut Fourier},
     pages = {1381--1385},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {65},
     number = {3},
     year = {2015},
     doi = {10.5802/aif.2960},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2960/}
}
TY  - JOUR
AU  - Jammes, Pierre
TI  - Une inégalité de Cheeger pour le spectre de Steklov
JO  - Annales de l'Institut Fourier
PY  - 2015
SP  - 1381
EP  - 1385
VL  - 65
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2960/
DO  - 10.5802/aif.2960
LA  - fr
ID  - AIF_2015__65_3_1381_0
ER  - 
%0 Journal Article
%A Jammes, Pierre
%T Une inégalité de Cheeger pour le spectre de Steklov
%J Annales de l'Institut Fourier
%D 2015
%P 1381-1385
%V 65
%N 3
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2960/
%R 10.5802/aif.2960
%G fr
%F AIF_2015__65_3_1381_0
Jammes, Pierre. Une inégalité de Cheeger pour le spectre de Steklov. Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1381-1385. doi : 10.5802/aif.2960. https://aif.centre-mersenne.org/articles/10.5802/aif.2960/

[1] Agranovich, M. S. On a mixed Poincaré-Steklov Type Spectral Problem in a Lipschitz Domain, Russ. J. Math. Phys., Volume 13 (2005) no. 3, pp. 239-244 | DOI | MR | Zbl

[2] Bandle, C. Isoperimetric inequalities and applications, Monographs and Studies in Mathematics, 7, Pitman, 1980 | MR | Zbl

[3] Brooks, R. The bottom of the spectrum of a Riemannian covering, J. Reine Angew. Math., Volume 357 (1985), pp. 101-114 | MR | Zbl

[4] Buser, P. On Cheeger inequality λ 1 ≥h 2 /4, Geometry of the Laplace operator (Proc. Sympos. Pure Math., XXXVI), Amer. Math. Soc., 1980, pp. 29-77 | MR | Zbl

[5] Cheeger, J. A lower bound for the smallest eigenvalue of the Laplacian, Problems in analysis (Papers dedicated to Salomon Bochner, 1969) (1970) | MR | Zbl

[6] Cheng, S.-Y.; Oden, K. Isoperimetric inequalities and the gap between the first and second eigenvalues of an Euclidean domain, J. Geom. Anal., Volume 7 (1997) no. 2, pp. 217-239 | DOI | MR | Zbl

[7] Colbois, B.; El Soufi, A.; Girouard, A. Isoperimetric control of the Steklov spectrum, J. Funct. Anal., Volume 261 (2011) no. 5, pp. 1384-1399 | DOI | MR | Zbl

[8] Escobar, J. F. The geometry of the first non-zero Stekloff eigenvalue, J. Funct. Anal., Volume 150 (1997) no. 2, pp. 544-556 | DOI | MR | Zbl

[9] Escobar, J. F. An isoperimetric Inequality and the first Steklov Eigenvalue, J. Funct. Anal., Volume 165 (1999) no. 1, pp. 101-116 | DOI | MR | Zbl

[10] Girouard, A.; Polterovich, I. On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues, Functional Analysis and its Applications, Volume 44 (2010) no. 2, pp. 106-117 | DOI | MR | Zbl

[11] Guérini, P. Prescription du spectre du laplacien de Hodge-de Rham, Ann. scient. Éc. norm. sup. (4), Volume 37 (2004) no. 2, pp. 270-303 | Numdam | MR | Zbl

[12] Krantz, S. T.; Parks, H. R. Geometric Integration Theory, Birkäuser, 2008 | MR | Zbl

[13] Sylvester, J.; Uhlmann, G. The Dirichlet to Neumann map and applications, Inverse problems in partial differential equations (Arcata, CA, 1989) (1990), pp. 101-139 | MR | Zbl

[14] Uhlmann, G. Electrical impedance tomography and Calderón’s problem, Inverse Problems, Volume 25 (2009) no. 12, pp. 123011, 39 | DOI | Zbl

Cité par Sources :