On the multiplicy of the eigenvalues of the Laplacian

Eigenvalues of the Laplacian on forms

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1982-0656119-2 ◽

1982 ◽

Vol 85 (3) ◽

pp. 437-437 ◽

Cited By ~ 16

Author(s):

Jozef Dodziuk

Keyword(s):

Eigenvalues Of The Laplacian

Eigenvalues of the Laplacian, the First Betti Number and the Congruence Subgroup Problem

Annals of Mathematics ◽

10.2307/2118597 ◽

1996 ◽

Vol 144 (2) ◽

pp. 441 ◽

Cited By ~ 17

Author(s):

Alexander Lubotzky

Keyword(s):

Betti Number ◽

Congruence Subgroup ◽

Eigenvalues Of The Laplacian ◽

Subgroup Problem ◽

Congruence Subgroup Problem

Eigenvalues of the Laplacian and the Heat Equation

American Mathematical Monthly ◽

10.2307/2320674 ◽

1981 ◽

Vol 88 (9) ◽

pp. 686 ◽

Cited By ~ 7

Author(s):

Jozef Dodziuk

Keyword(s):

Heat Equation ◽

Eigenvalues Of The Laplacian

Extrema of Low Eigenvalues of the Dirichlet–Neumann Laplacian on a Disk

Canadian Journal of Mathematics ◽

10.4153/cjm-2010-042-8 ◽

2010 ◽

Vol 62 (4) ◽

pp. 808-826

Author(s):

Eveline Legendre

Keyword(s):

Boundary Conditions ◽

Mixed Boundary ◽

Neumann Boundary ◽

Mixed Boundary Conditions ◽

First Eigenvalue ◽

Bounded Number ◽

Eigenvalues Of The Laplacian ◽

Neumann Laplacian ◽

Dirichlet And Neumann Conditions ◽

Second Eigenvalue

AbstractWe study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet–Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.

Eigenvalues of the Laplacian on wildly perturbed domain

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.58.419 ◽

1982 ◽

Vol 58 (10) ◽

pp. 419-421 ◽

Cited By ~ 2

Author(s):

Shin Ozawa

Keyword(s):

Eigenvalues Of The Laplacian

On the growth of the eigenvalues of the Laplacian operator in a quasibounded domain

Archive for Rational Mechanics and Analysis ◽

10.1007/bf00251416 ◽

1968 ◽

Vol 31 (5) ◽

pp. 352-356 ◽

Cited By ~ 8

Author(s):

Colin Clark

Keyword(s):

Laplacian Operator ◽

Eigenvalues Of The Laplacian

The second term of the asymptotic distribution of eigenvalues of the laplacian in the polygonal domain

Communications in Partial Differential Equations ◽

10.1080/03605308308820321 ◽

1983 ◽

Vol 8 (15) ◽

pp. 110-117

Author(s):

Ken'ichi Otsuka

Keyword(s):

Asymptotic Distribution ◽

Polygonal Domain ◽

Distribution Of Eigenvalues ◽

Eigenvalues Of The Laplacian

Shape Recognition Based on Eigenvalues of the Laplacian

Advances in Imaging and Electron Physics ◽

10.1016/b978-0-12-385985-3.00003-1 ◽

2011 ◽

pp. 185-254 ◽

Cited By ~ 1

Author(s):

Mohamed Ben Haj Rhouma ◽

Mohamed Ali Khabou ◽

Lotfi Hermi

Keyword(s):

Shape Recognition ◽

Eigenvalues Of The Laplacian

The eigenvalues of the Laplacian with Dirichlet boundary condition in $$\mathbb {R}^2$$ R 2 are almost never minimized by disks

Annals of Global Analysis and Geometry ◽

10.1007/s10455-014-9446-9 ◽

2014 ◽

Vol 47 (3) ◽

pp. 285-304 ◽

Cited By ~ 13

Author(s):

Amandine Berger

Keyword(s):

Boundary Condition ◽

Dirichlet Boundary Condition ◽

Dirichlet Boundary ◽

Eigenvalues Of The Laplacian

Eigenvalues of the Laplacian for Hecke triangle groups

Memoirs of the American Mathematical Society ◽

10.1090/memo/0469 ◽

1992 ◽

Vol 97 (469) ◽

pp. 0-0 ◽

Cited By ~ 15

Author(s):

Dennis A. Hejhal

Keyword(s):

Triangle Groups ◽

Eigenvalues Of The Laplacian