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＜電子ブック＞
Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets / by José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2019.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2019
大きさ	XVIII, 123 p. 2 illus., 1 illus. in color : online resource
著者標目	*Mazón, José M author Rossi, Julio Daniel author Toledo, J. Julián author SpringerLink (Online service)
件　名	LCSH:Integral equations LCSH:Measure theory LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations FREE:Integral Equations FREE:Measure and Integration FREE:Calculus of Variations and Optimization FREE:Differential Equations
一般注記	Nonlocal Perimeter -- Nonlocal Isoperimetric Inequality -- Nonlocal Minimal Surfaces and Nonlocal Curvature -- Nonlocal Operators -- Nonlocal Cheeger and Calibrable Sets -- Nonlocal Heat Content -- A Nonlocal Mean Curvature Flow -- Bibliography -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-030-06243-9

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