Ozawa, Shin; Roppongi, Susumu Singular variation of domain and eigenvalues of the Laplacian with the third boundary condition. (English) Zbl 0838.35089 Proc. Japan Acad., Ser. A 68, No. 7, 186-189 (1992). The authors continue the study of [the first author, Osaka J. Math. 29, No. 4, 837-850 (1992; Zbl 0802.35111)]. The results here are stated without proofs. Cited in 2 Documents MSC: 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35B25 Singular perturbations in context of PDEs Citations:Zbl 0802.35111 PDFBibTeX XMLCite \textit{S. Ozawa} and \textit{S. Roppongi}, Proc. Japan Acad., Ser. A 68, No. 7, 186--189 (1992; Zbl 0838.35089) Full Text: DOI References: [1] C. Anne: Spectre du laplacien et ecrasement d’ansens. Ann. Sci. Ecole Norm. Sup., 20, 271-280 (1987). · Zbl 0634.58035 [2] J. M. Arrieta, J. Hale, and Q. Han: Eigenvalue problems for nonsmoothly perturbed domains. J. Diff. Equations, 91, 24-52 (1991). · Zbl 0736.35073 [3] G. Besson : Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou. Bull. Soc. Math. France, 113, 211-239 (1985). · Zbl 0577.58033 [4] I. Chavel: Eigenvalues in Riemannian Geometry. Academic Press (1984). · Zbl 0551.53001 [5] S. Jimbo: The singularly perturbed domain and the characterization for the eigen-functions with Neumann boundary condition. J. Diff. Equations, 77, 322-350 (1989). · Zbl 0703.35138 [6] S. Ozawa: Singular variation of domain and spectra of the Laplacian with small Robin coditional boundary. I (to appear in Osaka J. Math.). · Zbl 0802.35111 [7] S. Ozawa: Spectra of domains with small spherical Neumann boundary. J. Fac. Sci. Univ. Tokyo, Sec. IA, 30, 259-277 (1983). · Zbl 0541.35061 [8] S. Ozawa: Asymptotic property of an eigenfunction of the Laplacian under singular variation of domains–the Neumann condition–. Osaka J. Math., 22, 639-655 (1985). · Zbl 0579.35065 [9] S. Ozawa: Electrostatic capacity and eigenvalues of the Laplacian. J. Fac. Sci. Univ. Tokyo, Sec. IA,30, 53-62 (1983). · Zbl 0531.35061 [10] J. Rauch and M. Taylor: potential and scattering theory on wildly perturbed domains. J. Funct. Anal., 19, 27-59 (1975). · Zbl 0293.35056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.