Real analytic families of harmonic functions in a planar domain with a small hole

M. Dalla Riva*, P. Musolino

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

12 Dyfyniadau(SciVal)

Crynodeb

We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ε and we denote by uε the corresponding solution. The behavior of uε for ε small and positive can be described in terms of real analytic functions of two variables evaluated at (ε, 1/log ε). We show that under suitable assumptions on the geometry and on the boundary data one can get rid of the logarithmic behavior displayed by uε for ε small and describe uε by real analytic functions of ε. Then it is natural to ask what happens when ε is negative. The case of boundary data depending on ε is also considered. The aim is to study real analytic families of harmonic functions which are not necessarily solutions of a particular boundary value problem.

Iaith wreiddiolSaesneg
Tudalennau (o-i)37-55
Nifer y tudalennau19
CyfnodolynJournal of Mathematical Analysis and Applications
Cyfrol422
Rhif cyhoeddi1
Dyddiad ar-lein cynnar22 Awst 2014
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 01 Chwef 2015

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