Interactions Between Moderately Close Inclusions for the Two-Dimensional Dirichlet–Laplacian | Zendy

Virginie BonnaillieNoël | Zendy; Marc Dambrine | Zendy; Christophe Lacave | Zendy

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Interactions Between Moderately Close Inclusions for the Two-Dimensional Dirichlet–Laplacian

Author(s) -

Virginie BonnaillieNoël,

Marc Dambrine,

Christophe Lacave

Publication year - 2015

Publication title -

applied mathematics research express

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.763

H-Index - 20

eISSN - 1687-1200

pISSN - 1687-1197

DOI - 10.1093/amrx/abv008

Subject(s) - dimension (graph theory) , laplace operator , mathematics , dirichlet distribution , conformal map , domain (mathematical analysis) , dirichlet eigenvalue , mathematical analysis , dirichlet problem , laplace transform , dirichlet's principle , pure mathematics , boundary value problem

International audienceThis paper concerns the asymptotic expansion of the solution of the Dirichlet-Laplace problem in a domain with small inclusions. This problem is well understood for the Neumann condition in dimension greater than two or Dirichlet condition in dimension greater than three. The case of two circular inclusions in a bidimensional domain was considered in [1]. In this paper, we generalize the previous result to any shape and relax the assumptions of regularity and support of the data. Our approach uses conformal mapping and suitable lifting of Dirichlet conditions. We also analyze configurations with several scales for the distance between the inclusions (when the number is larger than 2)

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