A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary

We also show how one can use this abstract formulation both for giving different and sim- pler proofs for all the known results obtained for the eigenvalues of a power of the

We consider the solution of an interface problem posed in a bounded domain coated with a layer of thickness ε and with external boundary conditions of Dirichlet or Neumann type..

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Some considerable difficulties arise at key turning points of our work, due to the nature of the system of nonlinear equations that we are dealing with, in particular in the

Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random

The main purpose of this work is to study and give optimal estimates for the Dirichlet problem for the biharmonic operator A 2 on an arbitrary bounded Lipschitz domain D in R\ with

This manuscript establishes, in the generic case, the existence and uniqueness of the solution for the Ventcel boundary value problem without the sign condition.. Then, we

Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the