15 citations · 33 across the 5 of their papers we have counts for
10 papers
On the parabolic Harnack inequality for non-local diffusion equations
Dominik Dier, Jukka Kemppainen, Juhana Siljander +1
We settle the open question concerning the Harnack inequality for globally positive solutions to non-local in time diffusion equations by constructing a counter-example for dimensi…
Discrete versions of the Li-Yau gradient estimate
Dominik Dier, Moritz Kassmann, Rico Zacher
We study positive solutions to the heat equation on graphs. We prove variants of the Li-Yau gradient estimate and the differential Harnack inequality. For some graphs, we can show…
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…
Non-Autonomous Forms and Invariance
Dominik Dier
We generalize the Beurling--Deny--Ouhabaz criterion for parabolic evolution equations governed by forms to the non-autonomous, non-homogeneous and semilinear case. Let are H…
Non-Autonomous Maximal Regularity in Hilbert Spaces
Dominik Dier, Rico Zacher
We consider non-autonomous evolutionary problems of the form , on , where is a Hilbert space. We do not assume that the domain of…
Non-Autonomous Maximal Regularity for Forms of Bounded Variation
Dominik Dier
We consider a non-autonomous evolutionary problem \[ u' (t)+\mathcal A (t)u(t)=f(t), \quad u(0)=u_0, \] where are Hilbert spaces such that is continuously and densely em…
Maximal Regularity for Non-Autonomous Second Order Cauchy Problems
Dominik Dier, El Maati Ouhabaz
We consider non-autonomous wave equations \[ \left\{ \begin{aligned} \&\ddot u(t) + \B(t)\dot u(t) + \A(t)u(t) = f(t) \quad t\text{-a.e.}\\ \&u(0)=u_0,\, \dot u(0) = u_1. \end{alig…
Invariance of Convex Sets for Non-autonomous Evolution Equations Governed by Forms
Wolfgang Arendt, Dominik Dier, El Maati Ouhabaz
We consider a non-autonomous form $\fra:[0,T]\times V\times V \to \C$ where is a Hilbert space which is densely and continuously embedded in another Hilbert space . Denote b…
Diffusion in networks with time-dependent transmission conditions
Wolfgang Arendt, Dominik Dier, Marjeta Kramar Fijavž
We study diffusion in a network which is governed by non-autonomous Kirchhoff conditions at the vertices of the graph. Also the diffusion coefficients may depend on time. We prove…
Maximal Regularity for Evolution Equations Governed by Non-Autonomous Forms
Wolfgang Arendt, Dominik Dier, Hafida Laasri +1
\begin{abstract}\label{abstract} We consider a non-autonomous evolutionary problem \[ \dot{u} (t)+\A(t)u(t)=f(t), \quad u(0)=u_0 \] where the operator $\A(t):V\to V^\prime$ is asso…