Asymptotic expansions for the conductivity problem with nearly touching inclusions with corner
Annales Henri Lebesgue, Volume 3 (2020) , pp. 381-406.

KeywordsAsymptotic expansion, corner singularity

### Abstract

We investigate the case of a medium with two inclusions or inhomogeneities with nearly touching corner singularities. We present two different asymptotic models to describe the phenomenon under specific geometrical assumptions. These asymptotic expansions are analysed and compared in a common framework. We conclude by a representation formula to characterise the detachment of the corners and we provide the possible extensions of the geometrical hypotheses.

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