Overview
- Contains the first systematic presentation of nonlocal curvature and perimeter for measurable sets
- With applications to minimal surfaces
- Nonlocal heat content is also studied
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (7 chapters)
Keywords
About this book
This book highlights the latest developments in the geometry of measurable sets, presenting them in simple, straightforward terms. It addresses nonlocal notions of perimeter and curvature and studies in detail the minimal surfaces associated with them.
These notions of nonlocal perimeter and curvature are defined on the basis of a non-singular kernel. Further, when the kernel is appropriately rescaled, they converge toward the classical perimeter and curvature as the rescaling parameter tends to zero. In this way, the usual notions can be recovered by using the nonlocal ones. In addition, nonlocal heat content is studied and an asymptotic expansion is obtained.
Given its scope, the book is intended for undergraduate and graduate students, as well as senior researchers interested in analysis and/or geometry.
Authors and Affiliations
Bibliographic Information
Book Title: Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets
Authors: José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-030-06243-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-06242-2Published: 29 April 2019
eBook ISBN: 978-3-030-06243-9Published: 10 April 2019
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XVIII, 123
Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour
Topics: Integral Equations, Measure and Integration, Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations