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.

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

Musolino P.
2016

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.
File in questo prodotto:
File Dimensione Formato  
LPDE_A_1135166.pdf

non disponibili

Dimensione 990.8 kB
Formato Adobe PDF
990.8 kB Adobe PDF   Visualizza/Apri

I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/3723526
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 5
social impact