Analysis of the heat kernel of the Dirichlet-to-Neumann operator

A.F.M. Ter Elst (1) , El Maati Ouhabaz (2)

1 Department of Mathematics [Auckland]
2 IMB - Institut de Mathématiques de Bordeaux

We prove Poisson upper bounds for the kernel $K$ of the semigroup generated by the Dirichlet-to-Neumann operator if the underlying domain is bounded and has a $C^\infty$-boundary. We also prove Poisson bounds for $K_z$ for all $z$ in the right half-plane and for all its derivatives.

Keywords: Poisson bounds; Dirichlet-to-Neumann operator; Poisson bounds.

Domains: Analysis of PDEs [math.AP]; Functional Analysis [math.FA]

A.F.M. Ter Elst, El Maati Ouhabaz. Analysis of the heat kernel of the Dirichlet-to-Neumann operator. Journal of Functional Analysis, 2014, 11, pp.4066-4109. ⟨hal-00797184⟩