A Variational Theory of Convolution-Type Functionals - Softcover

Alicandro, Roberto; Ansini, Nadia; Braides, Andrea

Softcover

ISBN 10: 9819906865 ISBN 13: 9789819906864

Publisher: Springer, 2023

Synopsis

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.

 

Edition details

• Publisher: Springer
• Publication date: 2023
• Language: English
• ISBN 10: 9819906865
• ISBN 13: 9789819906864
• Binding: Paperback
• Number of pages: 126