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Dimension reduction for −Δ1

Published online by Cambridge University Press:  03 September 2013

Maria Emilia Amendola ,
Giuliano Gargiulo  and
Elvira Zappale
Maria Emilia Amendola
Affiliation:
Dipartimento di Matematica, Universita’ degli Studi di Salerno, via Ponte Don Melillo, 84084 Fisciano (SA), Italy. emamendola@unisa.it
Giuliano Gargiulo
Affiliation:
DSBGA, Universita’ del Sannio, Benevento Italy; ggargiul@unisannio.it
Elvira Zappale
Affiliation:
Dipartimento di Ingegneria Industriale, Universita’ degli Studi di Salerno, via Ponte Don Melillo, 84084 Fisciano (SA), Italy; ezappale@unisa.it

Abstract

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A 3D-2D dimension reduction for −Δ1 is obtained. A powerlaw approximation from −Δp asp → 1 in terms of Γ-convergence, duality andasymptotics for least gradient functions has also been provided.

Keywords

1–LaplacianΓ–convergenceleast gradient functionsdimension reductionduality

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 1 , January 2014 , pp. 42 - 77
Copyright
© EDP Sciences, SMAI, 2013

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