71 citations · 177 across the 16 of their papers we have counts for
16 papers
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…
The Perron solution for elliptic equations without the maximum principle
W. Arendt, A. F. M. ter Elst, M. Sauter
In this article we consider the Dirichlet problem on a bounded domain with respect to a second-order elliptic differential operator in divergence form. We do n…
Construction of dynamical semigroups by a functional regularisation à la Kato
A. F. M. ter Elst, Valentin A. Zagrebnov
A functional version of the Kato one-parametric regularisation for the construction of a dynamical semigroup generator of a relative bound one perturbation is introduced. It does n…
Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator
W. Arendt, A. F. M. ter Elst, M. Warma
In the very influential paper \cite{CS07} Caffarelli and Silvestre studied regularity of , , by identifying fractional powers with a certain Dirichlet-to-Neumann ope…
Nonseparability and von Neumann's theorem for domains of unbounded operators
A. F. M. ter Elst, Manfred Sauter
A classical theorem of von Neumann asserts that every unbounded self-adjoint operator in a separable Hilbert space is unitarily equivalent to an operator in such th…
A generalisation of the form method for accretive forms and operators
A. F. M. ter Elst, Manfred Sauter, Hendrik Vogt
The form method as popularised by Lions and Kato is a successful device to associate m-sectorial operators with suitable elliptic or sectorial forms. McIntosh generalised the form…
The regular part of second-order differential sectorial forms with lower-order terms
A. F. M. ter Elst, Manfred Sauter
We present a formula for the regular part of a sectorial form that represents a general linear second-order differential expression that may include lower-order terms. The formula…
On series of sectorial forms
C. J. K. Batty, A. F. M. ter Elst
We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.
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 …
Square roots of perturbed subelliptic operators on Lie groups
Lashi Bandara, A. F. M. ter Elst, Alan McIntosh
We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators…
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…
Sectorial forms and degenerate differential operators
W. Arendt, A. F. M. ter Elst
If is a densely defined sectorial form in a Hilbert space which is possibly not closable, then we associate in a natural way a holomorphic semigroup generator with . This al…
Uniform subellipticity
A. F. M. ter Elst, Derek W. Robinson
We establish two global subellipticity properties of positive symmetric second-order partial differential operators on $L_2(\Ri^d)$. First, if $m \in \Ni$ then we consider operator…
Dirichlet forms and degenerate elliptic operators
A. F. M. ter Elst, Derek W. Robinson, Adam Sikora +1
It is shown that the theory of real symmetric second-order elliptic operators in divergence form on $\Ri^d$ can be formulated in terms of a regular strongly local Dirichlet form ir…
Second-order operators with degenerate coefficients
A. F. M. ter Elst, Derek W. Robinson, Adam Sikora +1
We consider properties of second-order operators on $\Ri^d$ with bounded real symmetric measurable coefficients. We assume…