Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization

Elena Beretta; Elisa Francini; Sergio Vessella

doi:10.1137/16M1082160

Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization

Elena Beretta, Elisa Francini, Sergio Vessella

Mathematics

Research output: Contribution to journal › Article

Abstract

In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.

Original language	English (US)
Pages (from-to)	756-776
Number of pages	21
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	2
DOIs	https://doi.org/10.1137/16M1082160
Publication status	Published - Jan 1 2017

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Keywords

Conductivity equation
Dirichlet to Neumann map
Polygonal inclusion
Shape derivative

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Cite this

Beretta, E., Francini, E., & Vessella, S. (2017). Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization. SIAM Journal on Mathematical Analysis, 49(2), 756-776. https://doi.org/10.1137/16M1082160

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10.1137/16M1082160