Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space

Luca Lussardi; Andrea Torricelli; Elvira Zappale; Luca Lussardi; Andrea Torricelli; Elvira Zappale

doi:10.3934/mine.2026012

Mathematics in Engineering

2026, Volume 8, Issue 3: 368-401. doi: 10.3934/mine.2026012

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Research article

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space

1.
Dipartimento di Scienze Matematiche G.L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy
2.
Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo, Italy
3.
Dipartimento di Scienze di base e Applicate per l'Ingegneria, Sapienza - Università di Roma, Via Antonio Scarpa 16, 00161 Roma, Italy and CIMA, Universidade de Évora, Portugal

Received: 21 August 2025 Revised: 16 April 2026 Accepted: 30 April 2026 Published: 08 May 2026

We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $ \Gamma $-convergence, providing an integral representation result in the space of manifold constrained functions with bounded variation.
- homogenization,
- dimensional reduction,
- manifold-valued spaces of functions with bounded variation,
- $ \Gamma $-convergence,
- micromagnetics,
- linear growth
Citation: Luca Lussardi, Andrea Torricelli, Elvira Zappale. Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space[J]. Mathematics in Engineering, 2026, 8(3): 368-401. doi: 10.3934/mine.2026012

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Abstract

We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $ \Gamma $-convergence, providing an integral representation result in the space of manifold constrained functions with bounded variation.

References

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