| Issue |
ESAIM: M2AN
Volume 52, Number 3, May–June 2018
|
|
|---|---|---|
| Page(s) | 1023 - 1049 | |
| DOI | https://doi.org/10.1051/m2an/2018021 | |
| Published online | 13 September 2018 | |
Density and trace results in generalized fractal networks
1
Institut des Sciences et Techniques de Valenciennes, University of Valenciennes,
Le Mont Houy,
59313
Valenciennes Cedex, France.
2
Fachgebiet Numerische Mathematik und Wissenschaftliches Rechnen, B-TU Cottbus-Senftenberg,
Platz der deutschen Einheit 1,
03046
Cottbus, Germany.
* Corresponding author: serge.nicaise@univ-valenciennes.fr
Received:
12
September
2017
Accepted:
16
March
2018
The first aim of this paper is to give different necessary and sufficient conditions that guarantee the density of the set of compactly supported functions into the Sobolev space of order one in infinite p-adic weighted trees. The second goal is to define properly a trace operator in this Sobolev space if it makes sense.
Mathematics Subject Classification: 35B53 / 35B40 / 35B65 / 35J05
Key words: Laplace equation / fractal / graph domain / Liouville property / boundary operator
© EDP Sciences, SMAI 2018
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