Advances in Differential Equations

An approximating family for the Dirichlet-to-Neumann semigroup

Abstract

In this paper we prove that the Dirichlet-to-Neumann semigroup $S(t)$ is an analytic compact Markov irreducible semigroup in $C(\partial \Omega)$ in any bounded smooth domain $\Omega$. By a generalization of the Lax semigroup, we construct an approximating family for $S(t)$. We prove some regularizing characters and compactness of this family. By using the ergodic properties of $S(t)$, we deduce its asymptotic behavior. At the end we conjecture some open problems.

Article information

Source
Adv. Differential Equations, Volume 11, Number 3 (2006), 241-257.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR2221482

Zentralblatt MATH identifier
1112.47032

Citation

Emamirad, Hassan; Laadnani, Idriss. An approximating family for the Dirichlet-to-Neumann semigroup. Adv. Differential Equations 11 (2006), no. 3, 241--257. https://projecteuclid.org/euclid.ade/1355867709