This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.
Author(s): Aldo Pratelli, Günter Leugering (eds.)
Series: International Series of Numerical Mathematics 166
Edition: 1
Publisher: Birkhäuser Basel
Year: 2015
Language: English
Pages: VIII, 314
Tags: Partial Differential Equations; Systems Theory, Control
Front Matter....Pages i-viii
On the Minimization of Area Among Chord-Convex Sets....Pages 1-17
Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity....Pages 19-41
On a Classical Spectral Optimization Problem in Linear Elasticity....Pages 43-55
Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions....Pages 57-101
A Phase Field Approach for Shape and Topology Optimization in Stokes Flow....Pages 103-115
An Overview on the Cheeger Problem....Pages 117-139
Shape- and Topology Optimization for Passive Control of Crack Propagation....Pages 141-197
Recent Existence Results for Spectral Problems....Pages 199-215
Approximate Shape Gradients for Interface Problems....Pages 217-227
Towards a Lagrange–Newton Approach for PDE Constrained Shape Optimization....Pages 229-249
Shape Optimization in Electromagnetic Applications....Pages 251-269
Shape Differentiability Under Non-linear PDE Constraints....Pages 271-300
Optimal Regularity Results Related to a Partition Problem Involving the Half-Laplacian....Pages 301-314
