Geodesic
Density and trace results in generalized fractal networks
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1023-1049.

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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.

DOI : 10.1051/m2an/2018021
Classification : 35B53, 35B40, 35B65, 35J05
Keywords: Laplace equation, fractal, graph domain, Liouville property, boundary operator

Nicaise, Serge 1 ; Semin, Adrien 1

1 
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Nicaise, Serge; Semin, Adrien. Density and trace results in generalized fractal networks. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1023-1049. doi : 10.1051/m2an/2018021. http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018021/

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