We investigate the behavior of the solution of a mixed problem for the Poisson equation in a domain with two moderately close holes. If ϱ1 and ϱ2 are two positive parameters, we define a perforated domain Ω(ϱ1,ϱ2) by making two small perforations in an open set: the size of the perforations is ϱ1ϱ2, while the distance of the cavities is proportional to ϱ1. Then, if r∗ is small enough, we analyze the behavior of the solution for (ϱ1,ϱ2) close to the degenerate pair (0,r∗).
We investigate the behavior of the solution of a mixed problem for the Poisson equation in a domain with two moderately close holes. If ϱ1 and ϱ2 are two positive parameters, we define a perforated domain Ω(ϱ1,ϱ2) by making two small perforations in an open set: the size of the perforations is ϱ1ϱ2, while the distance of the cavities is proportional to ϱ1. Then, if r∗ is small enough, we analyze the behavior of the solution for (ϱ1,ϱ2) close to the degenerate pair (0,r∗). Copyright © 2016 John Wiley & Sons, Ltd.
Moderately close Neumann inclusions for the Poisson equation
Musolino P.
2018-01-01
Abstract
We investigate the behavior of the solution of a mixed problem for the Poisson equation in a domain with two moderately close holes. If ϱ1 and ϱ2 are two positive parameters, we define a perforated domain Ω(ϱ1,ϱ2) by making two small perforations in an open set: the size of the perforations is ϱ1ϱ2, while the distance of the cavities is proportional to ϱ1. Then, if r∗ is small enough, we analyze the behavior of the solution for (ϱ1,ϱ2) close to the degenerate pair (0,r∗).
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