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This book presents a series of lectures on three of the best known
examples of free discontinuity problems: the Mumford-Shah model for
image segmentation, a variational model for the epitaxial growth of
thin films, and the sharp interface limit of the Ohta-Kawasaki
model for pattern formation in dyblock copolymers.
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-Nurnberg 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.
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-Nurnberg 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.
Recently much attention has been devoted to the optimization of
transportation networks in a given geographic area. One assumes the
distributions of population and of services/workplaces (i.e. the
network's sources and sinks) are known, as well as the costs of
movement with/without the network, and the cost of
constructing/maintaining it. Both the long-term optimization and
the short-term, "who goes where," optimization are considered.
These models can also be adapted for the optimization of other
types of networks, such as telecommunications, pipeline or drainage
networks. In the monograph we study the most general problem
settings, namely, when neither the shape nor even the topology of
the network to be constructed is known a priori.
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