343 citations
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math.AP2019★ 13 cited
A mixed problem for the Laplace operator in a domain with moderately close holes
Matteo Dalla Riva, Paolo Musolino
We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter and we define a perforated domain…
math.AP2017
The Dirichlet problem in a planar domain with two moderately close holes
M. Dalla Riva, P. Musolino
We investigate a Dirichlet problem for the Laplace equation in a domain of with two small close holes. The domain is obtained by making in a bounded open set two per…
math.AP2017★ 14 cited
Converging expansions for Lipschitz self-similar perforations of a plane sector
Martin Costabel, Matteo Dalla Riva, Monique Dauge +1
In contrast with the well-known methods of matching asymptotics and multiscale (or compound) asymptotics, the " functional analytic approach " of Lanza de Cristoforis (Analysis 28,…