Semi-classical analysis of the Laplace operator with Robin boundary conditions
نویسندگان
چکیده
منابع مشابه
The Saint-Venant inequality for the Laplace operator with Robin boundary conditions∗
This survey paper is focused on the Saint-Venant inequality for the Laplace operator with Robin boundary conditions. In a larger context, we make the point on the recent advances concerning isoperimetric inequalities of Faber-Krahn type for elastically supported membranes and describe the main ideas of their proofs in both contexts of rearrangement and free discontinuity techniques.
متن کاملEigenvalues of the Laplace operator with nonlinear boundary conditions ∗
An eigenvalue problem on a bounded domain for the Laplacian with a nonlinear Robin-like boundary condition is investigated. We prove the existence, isolation and simplicity of the first two eigenvalues. 2000 Mathematics Subject Classification: 35P30, 35D05, 35J60, 35J70, 58E05.
متن کاملMinimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions
In this paper, we are interested in the minimization of the second eigenvalue of the Laplacian with Dirichlet boundary conditions amongst convex plane domains with given area. The natural candidate to be the optimum was the “stadium”, convex hull of two identical tangent disks. We refute this conjecture. Nevertheless, we prove existence of a minimzer. We also study some qualitative properties o...
متن کاملStraight Quantum Waveguide with Robin Boundary Conditions⋆
Abstract. We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we localize the essential spectrum and derive a sufficient condition which guarantees the existence of bound states. Further properties of the associated...
متن کاملThe boundary sine-Gordon theory: classical and semi-classical analysis
We consider the sine-Gordon model on a half-line, with an additional potential term of the form −M cos β2 (φ − φ0) at the boundary. We compute the classical time delay for general values of M , β and φ0 using τ -function methods and show that in the classical limit, the method of images still works, despite the non-linearity of the problem. We also perform a semi-classical analysis, and find ag...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of Mathematical Sciences
سال: 2012
ISSN: 1664-3607,1664-3615
DOI: 10.1007/s13373-012-0028-5