Robert Haller-Dintelmann

The Kato square root problem follows from an extrapolation property of the Laplacian

On a domain

Maximal Parabolic Regularity for Divergence Operators on Distribution Spaces

\Omega \subseteq \mathbb{R}^d

Expansions in Generalized Eigenfunctions of the Weighted Laplacian on Star-shaped Networks

we consider second order elliptic systems in divergence form with bounded complex coefficients, realized via a sesquilinear form with domain

THE INFLUENCE OF THE TUNNEL EFFECT ON L ∞ -TIME DECAY

V \subseteq H^1(\Omega)

Energy Flow Above the Threshold of Tunnel Effect

. Under very mild assumptions on

Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems

\Omega

Elliptic model problems including mixed boundary conditions and material heterogeneities

and

Lp - Lq Estimates for parabolic systems in non-divergence form with VMO coefficients

V

The square root problem for second-order, divergence form operators with mixed boundary conditions on L p

we show that the Kato Square Root Problem for such systems can be reduced to a regularity result for the fractional powers of the negative Laplacian in the same geometric setting. This extends an earlier result of McIntosh to non-smooth coefficients.

The Kato Square Root Problem for mixed boundary conditions

We show that elliptic second-order operators A of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of A are discontinuous and A is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.