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Publication details

Document type
Other

Document subtype
Preprint

Title
Donati representation theorem for periodic functions in relation to homogenization theory

Participants in the publication
Cristian Barbarosie (Author)
Dep. Matemática
Anca-Maria Toader (Author)
Dep. Matemática
CMAFcIO

Summary
This paper discusses properties of periodic functions, focusing on (systems of) partial differential equations with periodicity boundary conditions, called "cellular problems". These cellular problems arise naturally from the asymptotic study of PDEs with rapidly oscillating coefficients; this study is called "homogenization theory". We believe the present paper may shed a new light on well-known concepts, for instance by showing hidden links between Green's formula, the div-curl lemma and Donati's representation theorem. We state and prove three extensions of Donati's Theorem adapted to the periodic framework which, beyond their own importance, are essential for understanding the variational formulations of cellular problems in strain, in stress and in displacement. Section 4 presents a self-contained study of properties of traces of a function and their relations with periodicity properties of that function.

Date of Submisson/Request
2022-09-14
Date of Publication
2022-09-14

Publication Identifiers

Document Identifiers
URL - https://doi.org/10.48550/arXiv.2209.06801

Keywords
periodic homogenization cellular problem Donati’s theorem


Export

APA
Cristian Barbarosie, Anca-Maria Toader, (2022). Donati representation theorem for periodic functions in relation to homogenization theory

IEEE
Cristian Barbarosie, Anca-Maria Toader, "Donati representation theorem for periodic functions in relation to homogenization theory", 2022

BIBTEX
@misc{61048, author = {Cristian Barbarosie and Anca-Maria Toader}, title = {Donati representation theorem for periodic functions in relation to homogenization theory}, year = 2022 }