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.
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},
year = {2014},
publisher = {EDP Sciences},
volume = {20},
number = {1},
doi = {10.1051/cocv/2013053},
zbl = {1288.35266},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2013053/}
}
TY - JOUR AU - Amendola, Maria Emilia AU - Gargiulo, Giuliano AU - Zappale, Elvira TI - Dimension reduction for $-\Delta _1$ JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 42 EP - 77 VL - 20 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2013053/ DO - 10.1051/cocv/2013053 LA - en ID - COCV_2014__20_1_42_0 ER -
%0 Journal Article %A Amendola, Maria Emilia %A Gargiulo, Giuliano %A Zappale, Elvira %T Dimension reduction for $-\Delta _1$ %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 42-77 %V 20 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2013053/ %R 10.1051/cocv/2013053 %G en %F COCV_2014__20_1_42_0
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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