New Trends in Shape Optimization

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.