Local and Nonlocal Zaremba Problems with Degenerate Weights

Anna Balci (Charles U, Prague)

Feb 26. 2025, 15:30 — 16:20

The Zaremba problem is a mixed boundary value problem where the Dirichlet condition is imposed on a set with positive capacity, as per Mazya's condition, rather than necessarily on a set of positive measure. This allows the Dirichlet condition to be defined on fractal-like sets, such as Cantor-type sets. We establish results for the local Zaremba problem for the Laplacian and the p-Laplacian with degenerate weights. For the nonlocal case, we propose a well-posed formulation of the Zaremba problem and derive foundational existence and regularity results. This talk is based on joint projects with Ho-Sik Lee (Bielefeld) and ongoing work with Guy Foghem (Dresden).

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Degenerate and Singular PDEs (Workshop)
Organizer(s):
Verena Bögelein (PLUS, Salzburg)
Ugo Gianazza (U of Pavia)
Juha Kinnunen (Aalto U)
Naian Liao (PLUS, Salzburg)