A variational theory of convolution-type functionals
著者
書誌事項
A variational theory of convolution-type functionals
（SpringerBriefs on PDEs and data science）
Springer, c2023
- : pbk
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注記
Other authors: Nadia Ansini, Andrea Braides, Andrey Piatnitski, Antonio Tribuzio
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
Preface
Introduction
Convolution-type energies
The -limit of a class of reference energies
Asymptotic embedding and compactness results
A compactness and integral-representation result
Periodic homogenization
A generalization and applications to point clouds
Stochastic homogenization
Application to convex gradient flows References
Index
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