The resolvent of a singularly perturbed elliptic operator
نویسندگان
چکیده
منابع مشابه
Regularization of A Singularly Perturbed Elliptic PDE
In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Four types of basic spectral regularization methods such as Showalter’s, Tikhonov’s, Lardy’s and Lavrentiev’s are applied to approximate the solution by introducing another large (or small) parameter. Convergence of the regularized solutions to t...
متن کاملThe resolvent trace of an elliptic cone operator
This note discusses some aspects of the analysis leading to the proof of the main theorem in [10] (stated here as Theorem 1) on the structure of the asymptotics of the resolvent trace of a general elliptic cone operator as the spectral parameter tends to infinity, under suitable minimal growth assumptions on the principal symbols of the operator. We deal with an elliptic cone differential operator
متن کاملAlmost Invariant Elliptic Manifolds in a Singularly Perturbed Hamiltonian System
We consider a singularly perturbed Hamiltonian system, which loses one degree of freedom at " = 0. Assume the slow manifold to be normally elliptic. In the case of an analytic Hamilton function it is shown that the slow manifold persists up to an exponentially small error term.
متن کاملThe Dirichlet Problem for Singularly Perturbed Elliptic Equations
There has been much work on various singularly perturbed partial differential equations or systems. Such equations or systems depend on some small parameters ε > 0, solutions denoted as uε. There are at least two types of questions being investigated. The first type is to study possible behavior of uε as ε tends to zero. The second is to actually construct, by various methods, such solutions. I...
متن کاملHomogenization of a One-Dimensional Spectral Problem for a Singularly Perturbed Elliptic Operator with Neumann Boundary Conditions
We study the asymptotic behavior of the rst eigenvalue and eigenfunction of a one-dimensional periodic elliptic operator with Neumann boundary conditions. The second order elliptic equation is not self-adjoint and is singularly perturbed since, denoting by ε the period, each derivative is scaled by an ε factor. The main di culty is that the domain size is not an integer multiple of the period. ...
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 Mathematical Analysis and Applications
سال: 1977
ISSN: 0022-247X
DOI: 10.1016/0022-247x(77)90104-4