Name: A Course In The Calculus Of Variations: Optimization Regularity And Modeling
Brand: Springer Verlag
SKU: 9783031450358
Price: 3834.0 INR
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A Course In The Calculus Of Variations: Optimization Regularity And Modeling

by Santambrogio , Filippo

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ISBN13: 9783031450358
Binding: Paperback
Subject: Mathematics and Statistics
Publisher: Springer Verlag
Publisher Imprint: Springer
Publication Date: January 1, 2023
Pages: 298
Original Price: EUR 54.99
Language: English
Edition: N/A
Item Weight: 508 grams
BISAC Subject(s): Applied, Functional Analysis, and Mathematical Analysis

About The Book

From the Back Cover
This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.
Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence.
While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

About The Author

Filippo Santambrogio is currently professor at Université Claude Bernard Lyon 1, after having completed his studies in Pisa and starting his career in Paris. He is a specialist of the calculus of variations and in particular optimal transport, mean field games, and gradient flows.

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