Eigenvalues and Resonances for Domains with Tubes: Neumann Boundary Conditions
نویسندگان
چکیده
منابع مشابه
Resonances and Balls in Obstacle Scattering with Neumann Boundary Conditions
We consider scattering by an obstacle in Rd, d ≥ 3 odd. We show that for the Neumann Laplacian if an obstacle has the same resonances as the ball of radius ρ does, then the obstacle is a ball of radius ρ. We give related results for obstacles which are disjoint unions of several balls of the same radius.
متن کاملLyapunov Inequalities for Neumann Boundary Conditions at Higher Eigenvalues
This paper is devoted to the study of Lyapunov-type inequality for Neumann boundary conditions at higher eigenvalues. Our main result is derived from a detailed analysis about the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the use of suitable minimization problems. This method of proof allows to obtain new information on Lyapunov constant...
متن کاملZeta Functions with Dirichlet and Neumann Boundary Conditions for Exterior Domains
We generalize earlier studies on the Laplacian for a bounded open domain 2 R 2 with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this same domain. Using single layer and double layer potentials we can prove a number of new relations which hold when one chooses independently Dirichlet or Neumann boundary con...
متن کاملINFINITELY MANY SOLUTIONS FOR A CLASS OF P-BIHARMONIC PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS
The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.
متن کاملNonlocal Problems with Neumann Boundary Conditions
We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...
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: Journal of Differential Equations
سال: 1995
ISSN: 0022-0396
DOI: 10.1006/jdeq.1995.1023