Buttazzo, G. ; Casas, E. ; de Teresa, L. ; Glowinski, R. ; Leugering, G. ; Trélat, E. ; Zhang, X.(éd.)
We prove uniform convergence in Lipschitz domains of approximations to p-harmonic functions obtained using the natural p-means introduced by Ishiwata, Magnanini, and Wadade [Calc. Var. Partial Differ. Equ. 56 (2017) 97]. We also consider convergence of natural means in the Heisenberg group in the case of smooth domains.
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Keywords: $$-Laplacian, natural $$-means, Dirichlet problem, Discrete approximations, asymptotic mean value properties, convergence, generalized viscosity solutions, Heisenberg group
@article{COCV_2021__27_1_A35_0,
author = {Manfredi, Juan J. and Stroffolini, Bianca},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {Convergence of the natural \protect\emph{p}-means for the {\protect\emph{p}-Laplacian}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021026},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021026/}
}
TY - JOUR AU - Manfredi, Juan J. AU - Stroffolini, Bianca ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - Convergence of the natural p-means for the p-Laplacian JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021026/ DO - 10.1051/cocv/2021026 LA - en ID - COCV_2021__27_1_A35_0 ER -
%0 Journal Article %A Manfredi, Juan J. %A Stroffolini, Bianca %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T Convergence of the natural p-means for the p-Laplacian %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021026/ %R 10.1051/cocv/2021026 %G en %F COCV_2021__27_1_A35_0
Manfredi, Juan J.; Stroffolini, Bianca. Convergence of the natural p-means for the p-Laplacian. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 33. doi: 10.1051/cocv/2021026
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Dedicated with admiration to our friend Enrique Zuazua on his 60$$-birthday.
