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

Matteo Dalla Riva, Paolo Musolino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (SciVal)

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 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.

Original languageEnglish
Pages (from-to)812-837
Number of pages26
JournalCommunications in Partial Differential Equations
Volume41
Issue number5
Early online date11 Jan 2016
DOIs
Publication statusPublished - 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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