25 citations · 97 across the 23 of their papers we have counts for
30 papers
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…
Semigroups generated by multivalued operators and domain convergence for parabolic problems
W. Arendt, I. Chalendar, B. Moletsane
The following version of the Lumer-Phillips is proved: a surjective dissipative operator is m-dissipative and invertible. The result remains true if dissipative linear relations (i…
Space-time error estimates for approximations of linear parabolic problems with generalized time boundary conditions
Wolfgang Arendt, Isabelle Chalendar, Robert Eymard
We first give a general error estimate for the nonconforming approximation of a problem for which a Banach-Ne{\v c}as-Babu{\v s}ka (BNB) inequality holds. This framework covers par…
Extensions of derivations and symmetric operators
Wolfgang Arendt, Isabelle Chalendar, Robert Eymard
Given a densely defined skew-symmetric operators A 0 on a real or complex Hilbert space V , we parametrize all m-dissipative extensions in terms of contractions : H-$\rightarro…
Lions' representation theorem and applications
Wolfgang Arendt, Isabelle Chalendar, Robert Eymard
The Representation Theorem of Lions (RTL) is a version of the Lax--Milgram Theorem where completeness of one of the spaces is not complete. In this paper, RTL is deduced from an op…
The Wentzell Laplacian via forms and the approximative trace
Wolfgang Arendt, Manfred Sauter
We use form methods to define suitable realisations of the Laplacian on a domain with Wentzell boundary conditions, i.e. such that holds…