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A variational theory of convolution-type functionals

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A variational theory of convolution-type functionalsby Roberto Alicandro ... [et al.].
其他作者:	Alicandro, Roberto.
出版者:	Singapore :Springer Nature Singapore :2023.
面頁冊數:	viii, 116 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Convolutions (Mathematics)
電子資源:	https://doi.org/10.1007/978-981-99-0685-7
ISBN:	9789819906857$q(electronic bk.)

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$q(electronic bk.)

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

246604
Convolutions (Mathematics)

LC Class. No.: QA601

Dewey Class. No.: 515.78

A variational theory of convolution-type functionals
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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.
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