4 papers
On the domains of first order differential operators on the Sierpiński gasket
Waldemar Schefer
We study the first order structure of -differential one-forms on the Sierpiński gasket. We consider piecewise energy finite functions related to one-forms, normal parts, and s…
Optimal Hölder regularity for solutions to Signorini-type obstacle problems
Ki-Ahm Lee, Se-Chan Lee, Waldemar Schefer
We study the existence, uniqueness, and regularity of weak solutions to a class of obstacle problems, where the obstacle condition can be imposed on a subset of the domain. In part…
On equations of continuity and transport type on metric graphs and fractals
Michael Hinz, Waldemar Schefer
We study first order equations of continuity and transport type on metric spaces of martingale dimension one, including finite metric graphs, p.c.f. self-similar sets and classical…
The Dirichlet Problem for Lévy-stable operators with -data
Florian Grube, Thorben Hensiek, Waldemar Schefer
We prove Sobolev regularity for distributional solutions to the Dirichlet problem for generators of -stable processes and exterior data, inhomogeneity in weighted -spaces.…