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＜E-Book＞
A Variational Theory of Convolution-Type Functionals / by Roberto Alicandro, Nadia Ansini, Andrea Braides, Andrey Piatnitski, Antonio Tribuzio
(SpringerBriefs on PDEs and Data Science. ISSN:27317609)

Edition	1st ed. 2023.
Publisher	Singapore : Springer Nature Singapore : Imprint: Springer
Year	2023
Language	English
Size	VIII, 116 p. 1 illus : online resource
Authors	*Alicandro, Roberto author Ansini, Nadia author Braides, Andrea author Piatnitski, Andrey author Tribuzio, Antonio author SpringerLink (Online service)
Subjects	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Integral equations LCSH:Functional analysis FREE:Calculus of Variations and Optimization FREE:Integral Equations FREE:Functional Analysis
Notes	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. HTTP:URL=https://doi.org/10.1007/978-981-99-0685-7

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