2023, Denk, Robert, Ploß, David, Rau, Sophia, Seiler, Jörg

2011, Denk, Robert, Seiler, Jörg

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.

2015, Denk, Robert, Seiler, Jörg

We investigate the R -boundedness of operator families belonging to the Boutet de Monvel calculus. In particular, we show that weakly and strongly parameter-dependent Green operators of nonpositive order are R -bounded. Such operators appear as resolvents of non-local (pseudodifferential) boundary value problems. As a consequence, we obtain maximal Lp -regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.

2010, Denk, Robert, Seiler, Jörg

We study maximal L_p-regularity for a class of pseudodifferential mixed order systems on a space-time cylinder ℝⁿ x ℝ or X x ℝ where X is a closed smooth manifold. To this end we construct a calculus of Volterra pseudodifferential operators and characterize the parabolicity of a system by the invertibility of certain associated symbols. A parabolic system is shown to induce isomorphisms between suitable L_p-Sobolev spaces of Bessel potential or Besov type. If the cross section of the space-time cylinder is compact, the inverse of a parabolic system belongs to the calculus again. As applications we discuss time-dependent Douglis-Nirenberg systems and a linear system arising in the study of the Stefan problem with Gibbs-Thomson correction.

2007, Denk, Robert, Seiler, Jörg

Skript zur Vorlesung vom Wintersemester 2007/08

2013, Denk, Robert, Seiler, Jörg

We investigate the R-boundedness of operator families belonging to the Boutet de Monvel calculus. In particular, we show that weakly and strongly parameter-dependent Green operators of nonpositive order are R-bounded. Such operators appear as resolvents of non-local (pseudodifferential) boundary value problems. As a consequence, we obtain maximal L_p-regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.

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

2007, Denk, Robert, Saal, Jürgen, Seiler, Jörg

Parameter-ellipticity with respect to a closed subsector of the complex plane for pseudodifferential Douglis-Nirenberg systems is introduced and shown to imply the existence of a bounded H_\infty-calculus in suitable scales of Sobolev, Besov, and Hölder spaces. We also admit non pseudodifferential perturbations. Applications concern systems with coefficients of mild Hölder regularity and the generalized thermoelastic plate equations.