A mixed problem for the Laplace operator in a domain with moderately close holes

We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter ε and we define a perforated domain Ωε obtained by making two small perforations in an open set. Both the size and the distance of the cavities tend to 0 as ε → 0. For ε small, we denote by uε the solution of a mixed problem for the Laplace equation in Ωε. We describe what happens to uε as ε → 0 in terms of real analytic maps and we compute an asymptotic expansion.

We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter epsilon and we define a perforated domain (epsilon) obtained by making two small perforations in an open set. Both the size and the distance of the cavities tend to 0 as epsilon 0. For epsilon small, we denote by u(epsilon) the solution of a mixed problem for the Laplace equation in (epsilon). We describe what happens to u(epsilon) as epsilon 0 in terms of real analytic maps and we compute an asymptotic expansion.