5 papers
Tangential and normal traces for extension domains with non-Lipschitz boundaries
Romain Cervera, Patrick Ciarlet, Anna Rozanova-Pierrat +1
We generalize the classical vector-valued tangential and normal trace theory on Lipschitz domains to the setting of non-Lipschitz -extension domains, which includes domains wi…
Layer potential operators for transmission problems on extension domains
Gabriel Claret, Michael Hinz, Anna Rozanova-Pierrat +1
We use the well-posedness of transmission problems on classes of two-sided Sobolev extension domains to give variational definitions for (boundary) layer potential operators and Ne…
Convergence of layer potentials and Riemann-Hilbert problem on extension domains
Gabriel Claret, Anna Rozanova-Pierrat, Alexander Teplyaev
We prove the convergence of layer potential operators for the harmonic transmission problem over a sequence of converging two-sided extension domains. Consequently, the Neumann-Poi…
Fractal curvatures and short-time asymptotics of heat content
Anna Rozanova-Pierrat, Alexander Teplyaev, Steffen Winter +1
The aim of our paper is twofold. First, we present new mathematical developments on the analysis of de Gennes' hypothesis on the short-time asymptotics of the heat content for boun…
Spectral properties of graphs associated to the Basilica group
Antoni Brzoska, Courtney George, Samantha Jarvis +2
We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the Basilica group, the iterated monodromy group of the quadratic polynomial $…