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

Elena Beretta, Elisa Francini, Sergio Vessella

Research output: Contribution to journalArticlepeer-review

Abstract

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)1862-1874
Number of pages13
JournalApplicable Analysis
Volume98
Issue number10
DOIs
StatePublished - Jul 27 2019

Keywords

  • 35J25
  • 35R30
  • 49N60
  • 49Q10
  • Polygonal inclusions
  • conductivity equation
  • shape derivative

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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