Volume 20, Number 1, January-March 2014
|Page(s)||42 - 77|
|Published online||03 September 2013|
Dimension reduction for −Δ1
Dipartimento di Matematica, Universita’ degli Studi di
Salerno, via Ponte Don
Fisciano ( SA), Italy
2 DSBGA, Universita’ del Sannio, Benevento Italy
3 Dipartimento di Ingegneria Industriale, Universita’ degli Studi di Salerno, via Ponte Don Melillo, 84084 Fisciano ( SA), Italy
Revised: 4 January 2013
A 3D-2D dimension reduction for −Δ1 is obtained. A power law approximation from −Δp as p → 1 in terms of Γ-convergence, duality and asymptotics for least gradient functions has also been provided.
Mathematics Subject Classification: 35J92 / 49J45 / 49K20 / 49M29
Key words: 1–Laplacian / Γ–convergence / least gradient functions / dimension reduction / duality
© EDP Sciences, SMAI, 2013
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