Titlebook: A Variational Theory of Convolution-Type Functionals; Roberto Alicandro,Nadia Ansini,Antonio Tribuzio Book 2023 The Editor(s) (if applicab

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Roberto Alicandro,Nadia Ansini,Antonio TribuzioGives an abstract framework for a comprehensive theory of convolution-type functionals.Provides an environment and technical tools to frame problems related to multiple-scale variational models.Introd

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Chemotherapeutica zur lokalen AnwendungIn this chapter we formalize the assumptions on our families of convolution-type functionals. Such assumptions are stated in terms of some growth and integrability conditions. We explain and comment these hypotheses comparing them with the corresponding assumptions for families of local integral functionals commonly used in the literature.

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Antioxidants/Antimutagens in FoodsThe main result of this chapter is a compactness and integral-representation result for the Γ-limits of the families {.(⋅, .)}., which we can obtain through a convolution version of the localization method of Γ-convergence. A key point is that it is possible to limit the analysis to finite-range convolutions through a truncation argument.

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M. Nagao,K. Wakabayashi,Y. Suwa,T. Kobayashis. The limit energy density is characterized by an asymptotic nonlocal homogenization formula, which reduces to a non-local cell-problem formula when the energy density is convex in the last variable. In the case of homogeneous integrands the homogenization formula simplify only in the convex case.

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