|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910768473303321 |
|
|
Autore |
Alicandro Roberto |
|
|
Titolo |
A Variational Theory of Convolution-Type Functionals / / Roberto Alicandro [and four others] |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Singapore : , : Springer, Springer Nature Singapore Pte Ltd., , [2023] |
|
©2023 |
|
|
|
|
|
|
|
|
|
ISBN |
|
9789819906857 |
9789819906840 |
|
|
|
|
|
|
|
|
Edizione |
[First edition.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (121 pages) |
|
|
|
|
|
|
Collana |
|
SpringerBriefs on PDEs and Data Science Series |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Convolutions (Mathematics) |
Variational principles |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references and index. |
|
|
|
|
|
|
Nota di contenuto |
|
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. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
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 |
|
|
|
|