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Homogenization of vectorial free-discontinuity functionals with cohesive type surface terms

Part of: Manifolds Numerical methods Stochastic processes Existence theories Homogenization, determination of effective properties

Published online by Cambridge University Press:  08 August 2025

Gianni Dal Maso  and
Davide Donati
Gianni Dal Maso
Affiliation:
SISSA, Via Bonomea, Trieste, Italy (dalmaso@sissa.it)
Davide Donati*
Affiliation:
SISSA, Via Bonomea, Trieste, Italy (ddonati@sissa.it)
*
*Corresponding author.
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Abstract

The results on Γ-limits of sequences of free-discontinuity functionals with bounded cohesive surface terms are extended to the case of vector-valued functions. In this framework, we prove an integral representation result for the Γ-limit, which is then used to study deterministic and stochastic homogenization problems for this type of functional.

Keywords

functionals depending on vector-valued functionsfree-discontinuity problemsΓ-convergencehomogenizationintegral representationstochastic homogenization

MSC classification

Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 49Q20: Variational problems in a geometric measure-theoretic setting 60G60: Random fields 74Q05: Homogenization in equilibrium problems 74S60: Stochastic methods

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 71
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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