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

Elena Beretta, Elisa Francini, Sergio Vessella

Research output: Contribution to journalArticle

### 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) 756-776 21 SIAM Journal on Mathematical Analysis 49 2 https://doi.org/10.1137/16M1082160 Published - Jan 1 2017

### Fingerprint

Dirichlet-to-Neumann Map
Shape Optimization
Shape optimization
Differentiability
Conductivity
Inclusion
Shape Derivative
Derivatives
Triangular
Optimization Problem
Derivative
Movement

### Keywords

• Conductivity equation
• Dirichlet to Neumann map
• Polygonal inclusion
• Shape derivative

### ASJC Scopus subject areas

• Analysis
• Computational Mathematics
• Applied Mathematics

### Cite this

Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization. / Beretta, Elena; Francini, Elisa; Vessella, Sergio.

In: SIAM Journal on Mathematical Analysis, Vol. 49, No. 2, 01.01.2017, p. 756-776.

Research output: Contribution to journalArticle

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