An analyticity result for the dependence of multiple eigenvalues and eigenspaces of the laplace operator upon perturbation of the domain

Pier Domenico Lamberti; Massimo Lanza de Cristoforis

doi:10.1017/S0017089502010157

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In this paper, we consider the dependence of the Dirichlet eigenvalues and eigenspaces of the Laplace operator upon perturbation of the domain of definition. We prove that the dependence of a certain eigenvalue and of the corresponding eigenspace is analytic on the set of perturbations that leave the multiplicity constant.

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Lamberti, Pier Domenico 2003. Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday. p. 741.

Cristoforis, M. Lanza de and Rossi, L. 2004. Real Analytic Dependence of Simple and Double Layer Potentials upon Perturbation of the Support and of the Density. Journal of Integral Equations and Applications, Vol. 16, Issue. 2,

Lamberti, Pier Domenico and Lanza de Cristoforis, Massimo 2006. Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains. Mathematical Physics, Analysis and Geometry, Vol. 9, Issue. 1, p. 65.

LAMBERTI, Pier Domenico and LANZA DE CRISTOFORIS, Massimo 2006. Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems. Journal of the Mathematical Society of Japan, Vol. 58, Issue. 1,

Khelifi, Abdessatar 2007. Asymptotic property and convergence estimation for the eigenelements of the Laplace operator. Applicable Analysis, Vol. 86, Issue. 10, p. 1249.

Burenkov, V. I. Lamberti, P. D. and Lanza de Cristoforis, M. 2008. Spectral stability of nonnegative self-adjoint operators. Journal of Mathematical Sciences, Vol. 149, Issue. 4, p. 1417.

Lamberti, Pier Domenico 2014. Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems. Complex Variables and Elliptic Equations, Vol. 59, Issue. 3, p. 309.

Buoso, Davide and Lamberti, Pier Domenico 2014. Shape deformation for vibrating hinged plates. Mathematical Methods in the Applied Sciences, Vol. 37, Issue. 2, p. 237.

Buoso, Davide and Lamberti, Pier Domenico 2015. New Trends in Shape Optimization. Vol. 166, Issue. , p. 43.

di Blasio, Giuseppina and Lamberti, Pier Domenico 2020. EIGENVALUES OF THE FINSLER p ‐LAPLACIAN ON VARYING DOMAINS . Mathematika, Vol. 66, Issue. 3, p. 765.

Lamberti, Pier Domenico and Zaccaron, Michele 2021. Shape sensitivity analysis for electromagnetic cavities. Mathematical Methods in the Applied Sciences, Vol. 44, Issue. 13, p. 10477.

Abatangelo, Laura Léna, Corentin and Musolino, Paolo 2022. Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains. Journal of Functional Analysis, Vol. 283, Issue. 12, p. 109718.

SUZUKI, Takashi and TSUCHIYA, Takuya 2024. Hadamard variation of eigenvalues with respect to general domain perturbations. Journal of the Mathematical Society of Japan, Vol. 76, Issue. 4,

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An analyticity result for the dependence of multiple eigenvalues and eigenspaces of the laplace operator upon perturbation of the domain

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