EAN: 9789819948666

SPRINGERBRIEFS ON PDES AND DATA SCIENCE OPTIM...

This book concerns the theory of optimal transport (OT) and its applications to solving
problems in geometric optics. It is a self-contained presentation including a detailed analysis
of the Monge problem  the Monge-Kantorovich problem  the transshipment problem  and the network
flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A
detailed analysis of the Wasserstein metric is also carried out. For the applications to optics
the book describes the necessary background concerning light refraction  solving both far-field
and near-field refraction problems  and indicates lines of current research in this area.
Researchers in the fields of mathematical analysis  optimal transport  partial differential
equations (PDEs)  optimization  and optics will find this book valuable. It is also suitable
for graduate students studying mathematics  physics  and engineering. The prerequisites for
this book include a solid understanding of measure theory and integration  as well as basic
knowledge of functional analysis.

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