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A Variational Theory of Convolution-Type Functionals
Andrey Piatnitski, Nadia Ansini, Andrea Braides, et al.
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Naturwissenschaften, Medizin, Informatik, Technik / Sonstiges
Beschreibung
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.
Kundenbewertungen
upscaling and spatial localization of non-local energies, gradient flows, peridynamics, integral-representation theorem, compactness theorems, hierarchical structured deformations, periodic homogenization, stochastic homogenization, point clouds, convolution functionals, non-local energies