Volume 27, 2021
Special issue in the honor of Enrique Zuazua's 60th birthday
|Number of page(s)||18|
|Published online||30 April 2021|
Convergence of the natural p-means for the p-Laplacian*
Department of Mathematics, University of Pittsburgh,
PA 15260, USA.
2 Department of Electrical Engineering and Information Technology, University Federico II Napoli, Napoli 80125, Italy.
** Corresponding author: firstname.lastname@example.org
Accepted: 4 March 2021
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.
Mathematics Subject Classification: 35J92 / 35D40 / 49L20 / 49L25 / 35R02 / 35B05 / 35J62
Key words: p-Laplacian / natural p-means / Dirichlet problem / Discrete approximations / asymptotic mean value properties / convergence / generalized viscosity solutions / heisenberg group
© EDP Sciences, SMAI 2021
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