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

Matteo Dalla Riva; Paolo Musolino

doi:10.1080/03605302.2015.1135166

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

Matteo Dalla Riva, Paolo Musolino^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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 Ω_ε 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 u_ε the solution of a mixed problem for the Laplace equation in Ω_ε. We describe what happens to u_ε as ε → 0 in terms of real analytic maps and we compute an asymptotic expansion.

Original language	English
Pages (from-to)	812-837
Number of pages	26
Journal	Communications in Partial Differential Equations
Volume	41
Issue number	5
Early online date	11 Jan 2016
DOIs	https://doi.org/10.1080/03605302.2015.1135166
Publication status	Published - 03 May 2016

Keywords

Asymptotic expansion
Laplace operator
mixed problem
moderately close holes
real analytic continuation in Banach space
singularly perturbed perforated domain

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N2 - 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.

AB - 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.

KW - Asymptotic expansion

KW - Laplace operator

KW - mixed problem

KW - moderately close holes

KW - real analytic continuation in Banach space

KW - singularly perturbed perforated domain

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 5

ER -

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

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