New Trends in Shape Optimization

ISBN-13: 9783319175621 / Angielski / Twarda / 2015 / 314 str.

Aldo Pratelli; Gunter Leugering

Opis

In this collection of essays one finds contributions from Davide Buoso, Giuseppe Buttazzo, Michel Delfour, Gianpaolo Leonardi, Dario Mazzoleni, Al-hassem Nayam, Alberto Paganini, Volker Schulz, Jan Sokolowski, Kevin Sturm, Michiel Van den Berg, Bozhidar Velichkov and Alessandro Zilio. New trends in Shape Optimization was the title of a Workshop that we have organized in Erlangen in September 2013. We have had a very interesting week with many contributions by both senior mathematicians and young students; in particular, many open problems have been described, and a fruitful spontaneous collaboration has started between many participants, in a very informal way and with the aid of a lot of coffee. Therefore, we have thought to organize this book, with each chapter written by a participant to the Workshop, often with some collaborator: here, the reader can find from survey papers to original articles. Some chapters deal with arguments of the talks of the Workshop, while others deal with arguments which have been described and discussed out of the official timetable. We hope that this book can give to each reader some flavour of the interesting week we have had."

Spis treści

Davide Buoso: “A few spectral optimization problems for elliptic equations and systems”.- Giuseppe Buttazzo: “Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity”.-  Michel Delfour: “Metrics spaces of shapes and geometries from set parametrized functions”.- Gianpaolo Leonardi.- Dario Mazzoleni.- Al-hassem Nayam: “Asymptotics of higher codimensional shapes and related problems”.- Alberto Paganini: “Approximate Shape Gradients for Interface Problems”.- Volker Schulz: “Towards a Lagrange-Newton Approach for PDE Constrained Shape Optimization”.- Jan Sokolowski: “Shape optimization for nonlinear PDEs”.- Kevin Sturm: “On the existence and identification of the shape derivative for PDE constrained problems”.- Michiel Van den Berg.- Bozhidar Velichkov.- Alessandro Zilio: “Optimal regularity results for a partition problem involving".

Blurb

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.