A transmission problem on a polygonal partition: regularity and shape differentiability

Elena Beretta, Elisa Francini, Sergio Vessella

Research output: Contribution to journalArticle


We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes of the partition. This allows to prove shape differentiability of solutions and to establish an explicit formula for the shape derivative.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalApplicable Analysis
StateAccepted/In press - May 3 2018



  • conductivity equation
  • Polygonal inclusions
  • shape derivative

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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