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A variational theory of convolution-...

Alicandro, Roberto.

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A variational theory of convolution-type functionals

Record Type:	Electronic resources : Monograph/item
Title/Author:	A variational theory of convolution-type functionals/ by Roberto Alicandro ... [et al.].
other author:	Alicandro, Roberto.
Published:	Singapore :Springer Nature Singapore : : 2023.,
Description:	viii, 116 p. :ill., digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction -- Chapter 2. Convolution-Type Energies -- Chapter 3. The Γ-limit of a Class of Reference Energies -- Chapter 4. Asymptotic Embedding and Compactness Results -- Chapter 5. A Compactness and Integral-Representation Result -- Chapter 6. Periodic Homogenization -- Chapter 7. A Generalization and Applications to Point Clouds -- Chapter 8. Stochastic Homogenization -- Chapter 9. Application to Convex Gradient Flows.
Contained By:	Springer Nature eBook
Subject:	Convolutions (Mathematics) -
Online resource:	https://doi.org/10.1007/978-981-99-0685-7
ISBN:	9789819906857

A variational theory of convolution-type functionals
A variational theory of convolution-type functionals[electronic resource] /by Roberto Alicandro ... [et al.]. - Singapore :Springer Nature Singapore :2023. - viii, 116 p. :ill., digital ;24 cm. - SpringerBriefs on PDEs and data science,2731-7609. - SpringerBriefs on PDEs and data science..

Chapter 1. Introduction -- Chapter 2. Convolution-Type Energies -- Chapter 3. The Γ-limit of a Class of Reference Energies -- Chapter 4. Asymptotic Embedding and Compactness Results -- Chapter 5. A Compactness and Integral-Representation Result -- Chapter 6. Periodic Homogenization -- Chapter 7. A Generalization and Applications to Point Clouds -- Chapter 8. Stochastic Homogenization -- Chapter 9. Application to Convex Gradient Flows.

This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science) The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.

ISBN: 9789819906857

Standard No.: 10.1007/978-981-99-0685-7doiSubjects--Topical Terms:

646444
Convolutions (Mathematics)

LC Class. No.: QA601

Dewey Class. No.: 515.78

A variational theory of convolution-type functionals
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245 0 2 $a A variational theory of convolution-type functionals $h [electronic resource] / $c by Roberto Alicandro ... [et al.].
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300 $a viii, 116 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs on PDEs and data science, $x 2731-7609
505 0 $a Chapter 1. Introduction -- Chapter 2. Convolution-Type Energies -- Chapter 3. The Γ-limit of a Class of Reference Energies -- Chapter 4. Asymptotic Embedding and Compactness Results -- Chapter 5. A Compactness and Integral-Representation Result -- Chapter 6. Periodic Homogenization -- Chapter 7. A Generalization and Applications to Point Clouds -- Chapter 8. Stochastic Homogenization -- Chapter 9. Application to Convex Gradient Flows.
520 $a This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science) The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.
650 0 $a Convolutions (Mathematics) $3 646444
650 0 $a Variational principles. $3 535297
650 1 4 $a Calculus of Variations and Optimization. $3 3538813
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650 2 4 $a Functional Analysis. $3 893943
700 1 $a Alicandro, Roberto. $3 3632395
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