Optimal Transport and Applications to Geometric Optics (SpringerBriefs on PDEs and Data Science) - Softcover

Gutiérrez, Cristian E.

 
9789819948666: Optimal Transport and Applications to Geometric Optics (SpringerBriefs on PDEs and Data Science)
Softcover
ISBN 10: 9819948665 ISBN 13: 9789819948666
Verlag: Springer, 2023

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.

Von der hinteren Coverseite

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 andintegration, as well as basic knowledge of functional analysis.


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Verlag
Springer
Erscheinungsdatum
2023
Sprache
Englisch
ISBN 10 
9819948665
ISBN 13 
9789819948666
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
148
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