An embedded trace theorem for infinite metric trees with applications to transmission problems with mixed dimensions.

06.12.2023, 13:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Konstantin Pankrashkin (Carl von Ossietzky Universität Oldenburg)

Abstract: For a class of weighted infinite metric trees we propose a definition of the boundary trace which maps H^1-functions on the tree to L^2-functions on a compact Riemannian manifold. For a range of parameters, the precise Sobolev regularity of the traces is determined. This allows one to show the well-posedness for a Laplace-type equation on infinite trees interacting with Euclidean domains through the boundary. Based on joint works with Valentina Franceschi (Padova), Maryna Kachanovska (Paris) and Kiyan Naderi (Oldenburg).