2 results for Arendt, W

  • Diffusion determines the manifold

    Arendt, W; Biegert, M; ter Elst, Antonius (2012)

    Journal article
    The University of Auckland Library

    We prove under a weak smoothness condition that two Riemannian manifolds are isomorphic if and only if there exists an order isomorphism which intertwines with the Dirichlet type heat semigroups on the manifolds.

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  • The Dirichlet-to-Neumann operator on rough domains

    Arendt, W; ter Elst, Antonius (2011)

    Journal article
    The University of Auckland Library

    We consider a bounded connected open set Ω⊂RdΩ⊂Rd whose boundary Γ has a finite (d−1)(d−1)-dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator D0D0 on L2(Γ)L2(Γ) by form methods. The operator −D0−D0 is self-adjoint and generates a contractive C0C0-semigroup S=(St)t>0S=(St)t>0 on L2(Γ)L2(Γ). We show that the asymptotic behaviour of StSt as t→∞t→∞ is related to properties of the trace of functions in H1(Ω)H1(Ω) which Ω may or may not have.

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