We consider the asymptotic behaviour of integral energies with convex integrands defined on one-dimensional networks contained in a region of the three-dimensional space with a fast-oscillating boundary as the period of the oscillation tends to zero, keeping the oscillation themselves of fixed size. The limit energy, obtained as a $Gamma$-limit with respect to an appropriate convergence, is defined in a `stratified' Sobolev space and is written as an integral functional depending on all, two or just one derivative, depending on the connectedness properties of the sublevels of the function describing the profile of the oscillations. In the three cases, the energy function is characterized through an usual homogenization formula for $p$-connected networks, a homogenization formula for thin-film networks and a homogenization formula for thin-rod networks, respectively
Homogenization of networks in domains with oscillating boundaries / Braides, Andrea; CHIADO' PIAT, Valeria. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 98:1-2(2019), pp. 45-63. [10.1080/00036811.2018.1430782]
Homogenization of networks in domains with oscillating boundaries
BRAIDES, ANDREA;CHIADO' PIAT, Valeria
2019
Abstract
We consider the asymptotic behaviour of integral energies with convex integrands defined on one-dimensional networks contained in a region of the three-dimensional space with a fast-oscillating boundary as the period of the oscillation tends to zero, keeping the oscillation themselves of fixed size. The limit energy, obtained as a $Gamma$-limit with respect to an appropriate convergence, is defined in a `stratified' Sobolev space and is written as an integral functional depending on all, two or just one derivative, depending on the connectedness properties of the sublevels of the function describing the profile of the oscillations. In the three cases, the energy function is characterized through an usual homogenization formula for $p$-connected networks, a homogenization formula for thin-film networks and a homogenization formula for thin-rod networks, respectivelyFile | Dimensione | Formato | |
---|---|---|---|
BCPZ.pdf
accesso aperto
Tipologia:
1. Preprint / submitted version [pre- review]
Licenza:
Pubblico - Tutti i diritti riservati
Dimensione
371.73 kB
Formato
Adobe PDF
|
371.73 kB | Adobe PDF | Visualizza/Apri |
Homogenization of networks in domains with oscillating boundaries.pdf
accesso riservato
Descrizione: articolo principale
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Non Pubblico - Accesso privato/ristretto
Dimensione
2.12 MB
Formato
Adobe PDF
|
2.12 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/2687249
Attenzione
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo