We provide a general treatment of a class of functionals modeled on convolution energies with integrable kernel. Such model energies approximate the p-th norm of the gradient as the kernel is scaled by letting a small parameter ε tend to 0. We first provide the necessary functional-analytic tools to show coerciveness of families of such functionals with respect to strong Lp convergence. The main result is a compactness and integral-representation theorem which shows that limits of convolution-type energies are local integral functionals with p-growth defined on a Sobolev space. This result is applied to obtain periodic homogenization results, to study applications to functionals defined on point-clouds, to stochastic homogenization and to the study of limits of the related gradient flows.

A Variational Theory of Convolution-Type Functionals / Alicandro, Roberto; Ansini, Nadia; Braides, Andrea; Piatnistski, Andrey; Tribuzio, Antonio. - (2022), pp. 1-107.

A Variational Theory of Convolution-Type Functionals

Nadia Ansini
;
2022

Abstract

We provide a general treatment of a class of functionals modeled on convolution energies with integrable kernel. Such model energies approximate the p-th norm of the gradient as the kernel is scaled by letting a small parameter ε tend to 0. We first provide the necessary functional-analytic tools to show coerciveness of families of such functionals with respect to strong Lp convergence. The main result is a compactness and integral-representation theorem which shows that limits of convolution-type energies are local integral functionals with p-growth defined on a Sobolev space. This result is applied to obtain periodic homogenization results, to study applications to functionals defined on point-clouds, to stochastic homogenization and to the study of limits of the related gradient flows.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1639912
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