Differentiability of the Dirichlet to Neumann Map Under Movements of Polygonal Inclusions with an Application to Shape Optimization

DOI10.1137/16M1082160zbMath1401.35337arXiv1606.08129OpenAlexW2573418627MaRDI QIDQ2967922

Elena Beretta, Sergio Vessella, Elisa Francini

Publication date: 9 March 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08129

zbMATH Keywords

Dirichlet to Neumann mapshape derivativeconductivity equationpolygonal inclusion

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Regularity of solutions in optimal control (49N60) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (6)

Inverse problems on low-dimensional manifolds ⋮ Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements ⋮ Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT ⋮ Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains ⋮ A transmission problem on a polygonal partition: regularity and shape differentiability ⋮ Lipschitz Stable Determination of Polygonal Conductivity Inclusions in a Two-Dimensional Layered Medium from the Dirichlet-to-Neumann Map

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