Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets

Kevin Arfi (1) , Anna Rozanova-Pierrat (1)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in $\mathbb{R}^n$, we generalize the definition of the Poincaré-Steklov operator to $d$-set boundaries, $n-2< d

Mots clés: Poincar\'e-Steklov operator; $d$-sets; Laplacian transport; fractal.

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]; Mathématiques [math]; Théorie spectrale [math.SP]

Kevin Arfi, Anna Rozanova-Pierrat. Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets. Discrete and Continuous Dynamical Systems - Series S, 2019, 12 (1), pp.1-26. ⟨10.3934/dcdss.2019001⟩. ⟨hal-01526951v2⟩