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.
General
Imprint: |
Springer Verlag, Singapore
|
Country of origin: |
Singapore |
Series: |
SpringerBriefs on PDEs and Data Science |
Release date: |
September 2023 |
First published: |
2023 |
Authors: |
Cristian E. Gutierrez
|
Dimensions: |
235 x 155mm (L x W) |
Edition: |
1st ed. 2023 |
ISBN-13: |
978-981-9948-66-6 |
Categories: |
Books
|
LSN: |
981-9948-66-5 |
Barcode: |
9789819948666 |
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