71 citations · 146 across the 8 of their papers we have counts for
8 papers
Elliptic systems generating a positive semigroup are decoupled
Wolfgang Arendt, A. F. M. ter Elst, Manfred Sauter
We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are rea…
Maximal regularity for generalized boundary conditions in time
Wolfgang Arendt, Manfred Sauter
We consider autonomous and non-autonomous evolution equations on a time interval in a Banach space with the non-standard time-boundary condition , where …
Nittka's invariance criterion and Hilbert space valued parabolic equations in
W. Arendt, A. F. M. ter Elst, M. Sauter
Nittka gave an efficient criterion on a form defined on which implies that the associated semigroup is -invariant for some given . We extend this cr…
Analytical aspects of isospectral drums
W. Arendt, A. F. M. ter Elst, J. B. Kennedy
We reexamine the proofs of isospectrality of the counterexample domains to Kac' question `Can one hear the shape of a drum?' from an analytical viewpoint. We reformulate isospectra…
The Dirichlet-to-Neumann operator via hidden compactness
W. Arendt, A. F. M. ter Elst, J. B. Kennedy +1
We show that to each symmetric elliptic operator of the form \[ \mathcal{A} = - \sum \partial_k \, a_{kl} \, \partial_l + c \] on a bounded Lipschitz domain …
The Dirichlet-to-Neumann operator on rough domains
W. Arendt, A. F. M. ter Elst
We consider a bounded connected open set whose boundary has a finite -dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operato…