25 citations · 97 across the 23 of their papers we have counts for
9 papers · 1 filter
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…
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…
Positive irreducible semigroups and their long-time behaviour
Wolfgang Arendt, Jochen Glück
The notion \emph{Perron-Frobenius theory} usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These int…
Elliptic problems and holomorphic functions in Banach spaces
Wolfgang Arendt, Manuel Bernhard, Marcel Kreuter
In the first part we show that a vector-valued almost separably valued function is holomorphic (harmonic) if and only if it is dominated by an function and t…
Generators of semigroups on Banach spaces inducing holomorphic semiflows
W. Arendt, I. Chalendar
Let be the generator of a -semigroup on a Banach space of analytic functions on the open unit disc. If consists of composition operators, then there exists a holom…
J. L. Lions' Problem on Maximal Regularity
Wolfgang Arendt, Dominik Dier, Stephan Fackler
This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results…