Waveguides with combined Dirichlet and Robin boundary conditions

作     者：Freitas, P. Krejcirik, D. 

作者机构：Univ Lisbon Dept Math Fac Motricidade Humana TU Lisbon Complexo InterdisciplinarAv Prof Gama Pinto 2 P-1649003 Lisbon Portugal Univ Lisbon Grp Math Phys P-1649003 Lisbon Portugal Acad Sci Czech Republ Dept Theoret Phys Inst Nucl Phys Prague 25068 Czech Republic 

出 版 物：《MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY》 (数理物理学、解析与几何)

年 卷 期：2006年第9卷第4期

页      面：335-352页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Grant Agency, (A100480501, IRP AV0Z10480505, LC06002) Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT Fundação para a Ciência e a Tecnologia, FCT, (POCI/-MAT/60863/2004, POCI2010, SFRH/BPD/11457/2002) Akademie Věd České Republiky, AV ČR 

主　　题：Dirichlet and Robin boundary conditions eigenvalues in strips and annuli Hardy inequality Laplacian waveguides 

摘      要：We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet-Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kriz (J. Phys. A, 35: L269-275, 2002).