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Nonlocal perimeter, curvature and mi...

Mazon, Jose M.

Nonlocal perimeter, curvature and minimal surfaces for measurable sets

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlocal perimeter, curvature and minimal surfaces for measurable setsby Jose M. Mazon, Julio Daniel Rossi, J. Julian Toledo.
Author:	Mazon, Jose M.
other author:	Rossi, Julio Daniel.
Published:	Cham :Springer International Publishing :2019.
Description:	xviii, 123 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Perimeters (Geometry)
Online resource:	https://doi.org/10.1007/978-3-030-06243-9
ISBN:	9783030062439$q(electronic bk.)

Nonlocal perimeter, curvature and minimal surfaces for measurable sets
Mazon, Jose M.

Nonlocal perimeter, curvature and minimal surfaces for measurable sets[electronic resource] /by Jose M. Mazon, Julio Daniel Rossi, J. Julian Toledo. - Cham :Springer International Publishing :2019. - xviii, 123 p. :ill., digital ;24 cm. - Frontiers in mathematics,1660-8046. - Frontiers in mathematics..

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.

ISBN: 9783030062439$q(electronic bk.)

Standard No.: 10.1007/978-3-030-06243-9doiSubjects--Topical Terms:

836551
Perimeters (Geometry)

LC Class. No.: QA465

Dewey Class. No.: 530.8

Nonlocal perimeter, curvature and minimal surfaces for measurable sets
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245 1 0 $a Nonlocal perimeter, curvature and minimal surfaces for measurable sets $h [electronic resource] / $c by Jose M. Mazon, Julio Daniel Rossi, J. Julian Toledo.
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300 $a xviii, 123 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in mathematics, $x 1660-8046
505 0 $a 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.
520 $a 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.
650 0 $a Perimeters (Geometry) $3 836551
650 0 $a Curvature. $3 340149
650 1 4 $a Integral Equations. $3 274836
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
650 2 4 $a Partial Differential Equations. $3 274075
700 1 $a Rossi, Julio Daniel. $3 836549
700 1 $a Toledo, J. Julian. $3 836550
710 2 $a SpringerLink (Online service) $3 273601
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830 0 $a Frontiers in mathematics. $3 558254
856 4 0 $u https://doi.org/10.1007/978-3-030-06243-9
950 $a Mathematics and Statistics (Springer-11649)