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

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

1 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

In the framework of the Laplacian transport, describing by a Robin boundary-valued problem in an exterior domain in R^n , we generalize the definition of the Poincaré-Steklov operator to d-set boundaries, n − 1 ≤ d < n , and give its spectral properties to compared to a the spectrum of the interior domain and also to a truncated domain, considered as an approximation of the exterior case. The well-posedness of the Robin boundary-valued problems for the truncated and exterior domains are obtained in the general framework of n-sets.

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Kevin Arfi, Anna Rozanova-Pierrat. Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets. 2017. ⟨hal-01526951v1⟩