Sharp Convergence Rate of Eigenvalues in a Domain with a Shrinking Tube
作者： Veronica Felli , Roberto Ognibene
DOI:
关键词:
摘要: In this paper we consider a class of singularly perturbed domains, obtained by attaching cylindrical tube to fixed bounded region and letting its section shrink zero. We use an Almgren-type monotonicity formula evaluate the sharp convergence rate simple eigenvalues, via Courant-Fischer Min-Max characterization blow-up analysis for scaled eigenfunctions.
harvard.edu
arxiv.org参考文章(25)
J.K. Hale, Eigenvalues and Perturbed Domains 10 Mathematical Essays on Approximation in Analysis and Topology. pp. 95- 123 ,(2005) , 10.1016/B978-044451861-3/50003-3
Philippe G. Ciarlet, Plates and Junctions in Elastic Multi-Structures ,(1990)
Ari Laptev, Timo Weidl, Hardy inequalities for magnetic Dirichlet forms Operator theory. ,vol. 108, pp. 299- 305 ,(1999) , 10.1007/978-3-0348-8745-8_28
Dan Henry, Antônio Luiz Pereira, Jack K. Hale, Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations ,(2005)
Neil S Trudinger, David G Gilbarg, Elliptic Partial Differential Equations of Second Order ,(2018)
A.B. Movchan, Multi-structures: asymptotic analysis and singular perturbation problems European Journal of Mechanics A-solids. ,vol. 25, pp. 677- 694 ,(2006) , 10.1016/J.EUROMECHSOL.2006.05.006
E. B. Davies, Eigenvalue stability bounds via weighted Sobolev spaces Mathematische Zeitschrift. ,vol. 214, pp. 357- 371 ,(1993) , 10.1007/BF02572409
K. Uhlenbeck, Generic Properties of Eigenfunctions American Journal of Mathematics. ,vol. 98, pp. 1059- ,(1976) , 10.2307/2374041
Daniel Daners, Dirichlet problems on varying domains Journal of Differential Equations. ,vol. 188, pp. 591- 624 ,(2003) , 10.1016/S0022-0396(02)00105-5
Shuichi Jimbo, The singularly perturbed domain and the characterization for the eigenfunctions with Neumann boundary condition Journal of Differential Equations. ,vol. 77, pp. 322- 350 ,(1989) , 10.1016/0022-0396(89)90147-2