21 citations · 71 across the 20 of their papers we have counts for
26 papers
Trace theory for parabolic boundary value problems with rough boundary conditions
Robert Denk, Floris B. Roodenburg
We characterise the trace spaces arising from intersections of weighted, vector-valued Sobolev spaces, where the weights are powers of the distance to the boundary. These weighted…
Martingales and Path-Dependent PDEs via Evolutionary Semigroups
Robert Denk, Markus Kunze, Michael Kupper
In this article, we develop a semigroup-theoretic framework for the analytic characterisation of martingales with path-dependent terminal conditions. Our main result establishes th…
-boundedness of Poisson operators
Robert Denk, Nick Lindemulder, Jörg Seiler
We investigate the -boundedness of parameter-dependent families of Poisson operators on the half-space in various scales of function spaces. Applications concern…
Evolutionary semigroups on path spaces
Robert Denk, Markus Kunze, Michael Kupper
We introduce the concept evolutionary semigroups on path spaces, generalizing the notion of transition semigroups to possibly non-Markovian stochastic processes. We study the basic…
Boundary value problems with rough boundary data
Robert Denk, David Ploß, Sophia Rau +1
We consider linear boundary value problems for higher-order parameter-elliptic equations, where the boundary data do not belong to the classical trace spaces. We employ a class of…
Convex monotone semigroups and their generators with respect to -convergence
Jonas Blessing, Robert Denk, Michael Kupper +1
We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to -convergence. In contrast to the linear theory, the domain…