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

10 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

Access to Document

10.1080/03605302.2015.1135166

Permanent link

Persistent link

Cite this

@article{c48e2fc9c0734ef489897c246f5019a9,

title = "A mixed problem for the Laplace operator in a domain with moderately close holes",

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.",

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

author = "{Dalla Riva}, Matteo and Paolo Musolino",

year = "2016",

month = may,

day = "3",

doi = "10.1080/03605302.2015.1135166",

language = "English",

volume = "41",

pages = "812--837",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor & Francis",

number = "5",

}

TY - JOUR

T1 - A mixed problem for the Laplace operator in a domain with moderately close holes

AU - Dalla Riva, Matteo

AU - Musolino, Paolo

PY - 2016/5/3

Y1 - 2016/5/3

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

UR - http://www.scopus.com/inward/record.url?scp=84962424401&partnerID=8YFLogxK

U2 - 10.1080/03605302.2015.1135166

DO - 10.1080/03605302.2015.1135166

M3 - Article

AN - SCOPUS:84962424401

SN - 0360-5302

VL - 41

SP - 812

EP - 837

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

Abstract

Keywords

Access to Document

Permanent link

Other files and links

Fingerprint

Cite this