We construct, on a 2 or 3-dimensional Riemannian manifold, the self-adjoint extensions of the Laplace operator restricted to the functions vanishing in some neigbhourhood of some point of . We compute explicitely the eigenvalues of .
On construit, sur une variété riemannienne de dimension ou , les extensions autoadjointes de la restriction du laplacien aux fonctions nulles au voisinage d’un point de . On calcule explicitement les valeurs propres de .
@article{AIF_1982__32_3_275_0, author = {Colin De Verdi\`ere, Yves}, title = {Pseudo-laplaciens. {I}}, journal = {Annales de l'Institut Fourier}, pages = {275--286}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {32}, number = {3}, year = {1982}, doi = {10.5802/aif.890}, mrnumber = {84k:58221}, zbl = {0489.58034}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.890/} }
Colin De Verdière, Yves. Pseudo-laplaciens. I. Annales de l'Institut Fourier, Volume 32 (1982) no. 3, pp. 275-286. doi : 10.5802/aif.890. http://www.numdam.org/articles/10.5802/aif.890/
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