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Nonlocal perimeter, curvature and mi...

Mazon, Jose M.

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Nonlocal perimeter, curvature and minimal surfaces for measurable sets

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Nonlocal perimeter, curvature and minimal surfaces for measurable sets/ by Jose M. Mazon, Julio Daniel Rossi, J. Julian Toledo.
作者:	Mazon, Jose M.
其他作者:	Rossi, Julio Daniel.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xviii, 123 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Perimeters (Geometry) -
電子資源:	https://doi.org/10.1007/978-3-030-06243-9
ISBN:	9783030062439

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

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

3386944
Perimeters (Geometry)

LC Class. No.: QA465

Dewey Class. No.: 530.8

Nonlocal perimeter, curvature and minimal surfaces for measurable sets
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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.
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650 0 $a Curvature. $3 711378
650 1 4 $a Integral Equations. $3 897446
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650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
650 2 4 $a Partial Differential Equations. $3 890899
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