Geodesic
Dimension reduction for -Δ 1
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, pp. 42-77

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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.

DOI : 10.1051/cocv/2013053
Classification : 35J92, 49J45, 49K20, 49M29
Keywords: 1-Laplacian, Γ-convergence, least gradient functions, dimension reduction, duality 
@article{COCV_2014__20_1_42_0,
     author = {Amendola, Maria Emilia and Gargiulo, Giuliano and Zappale, Elvira},
     title = {Dimension reduction for $-\Delta _1$},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {42--77},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {1},
     year = {2014},
     doi = {10.1051/cocv/2013053},
     zbl = {1288.35266},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013053/}
}
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Amendola, Maria Emilia; Gargiulo, Giuliano; Zappale, Elvira. Dimension reduction for $-\Delta _1$. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, pp. 42-77. doi: 10.1051/cocv/2013053

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