Nonlocal perimeter, curvature and minimal surfaces for measurable sets [Documento eletrónico] / José M. Mazón, Julio Daniel Rossi, J. Julián Toledo
Language: eng.Country: Switzerland, Swiss Confederation.Publication: Cham : Springer International Publishing, Birkhäuser, 2019Description: XVIII, 123 p. : il.ISBN: 978-3-030-06243-9.Series: Frontiers in MathematicsSubject - Topical Name: Integral equations | Measure theory | Mathematical optimization | Calculus of variations | Differential equations Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA431.SPR FCT (Browse shelf(Opens below)) | 1 | Available | 96102 |
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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