2009, Denk, Robert, Faierman, Melvin

This paper is concerned with a boundary value problem defined over a bounded region of Euclidean space, and in particular it is devoted to the establishment of a priori estimates for solutions of a parameter-elliptic multi-order system of differential equations under limited smoothness assumptions. In this endeavour we extend the results of Agranovich, Denk, and Faierman pertaining to a priori estimates for solutions associated with a parameter-elliptic scalar problem, as well as the results of various other authors who have extended the results of Agranovich et. al. from the scalar case to parameter-elliptic systems of operators which are either of homogeneous type or have the property that the diagonal operators are all of the same order. In addition, we extend some results of Kozhevnikov and Denk and Volevich who have also dealt with sytems of the kind under consideration here, in that one of the works of Kozhevnikov deals only with 2x2 systems, while the other, as well as the work of the last two authors, do not cover Dirichlet boundary conditions.

2009, Denk, Robert, Saal, Jürgen, Seiler, Jörg

2008, Denk, Robert, Racke, Reinhard, Shibata, Yoshihiro

2007, Denk, Robert, Seiler, Jörg

Skript zur Vorlesung vom Wintersemester 2007/08

2009, Denk, Robert, Mennicken, Reinhard

2008, Denk, Robert, Prüss, Jan, Zacher, Rico

In this paper we investigate vector-valued parabolic initial boundary value problems of relaxation type. Typical examples for such boundary conditions are dynamic boundary conditions or linearized free boundary value problems like in the Stefan problem. We present a complete Lp -theory for such problems which is based on maximal regularity of certain model problems.

2008, Denk, Robert, Volevič, Leonid R.

A new class of boundary value problems for parabolic operators is introduced which is based on the Newton polygon method. We show unique solvability and a priori estimates in corresponding L₂-Sobolev spaces. As an application, we discuss some linearized free boundary problems arising in crystallization theory which do not satisfy the classical parabolicity condition. It is shown that these belong to the new class of parabolic boundary value problems, and two-sided estimates for their solutions are obtained.

2009, Denk, Robert

In this note we discuss mathematical principles which are used by today's mobile communication systems. Among others, orthogonality, calculations in finite fields, and stochastic concepts are introduced. This note is based on a public lecture at the University of Regensburg.

2008, Denk, Robert, Racke, Reinhard, Shibata, Yoshihiro

In this paper we prove frequency expansions of the resolvent and local energy decay estimates for the linear thermoelastic plate equations subject to Dirichlet boundary conditions and initial conditions. The equation is considered in an exterior domain (domain with bounded complement) in the two- and three-dimensional space.

2008, Denk, Robert, Saal, Jürgen, Seiler, Jörg

We prove a maximal regularity result for operators corresponding to rotation invariant symbols (in space) which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary-value problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining it with abstract results on the H∞-calculus and R-bounded operator families. As an application, we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction.