EAN: 9789819906840

SPRINGERBRIEFS ON PDES AND DATA SCIENCE A VAR...

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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