16 citations · 87 across the 36 of their papers we have counts for
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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…
Restriction estimates via the derivatives of the heat semigroup and connexion with dispersive estimates
Frederic Bernicot, El Maati Ouhabaz
We consider an abstract non-negative self-adjoint operator on an -space. We derive a characterization for the restriction estimate $\| dE_H(λ) \|_{L^p \to L^{p'}} \le C λ^…
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…
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…
Analysis of the heat kernel of the Dirichlet-to-Neumann operator
A. F. M. ter Elst, E. M. Ouhabaz
We prove Poisson upper bounds for the kernel of the semigroup generated by the Dirichlet-to-Neumann operator if the underlying domain is bounded and has a -boundary.…