Università degli Studi di Padova

“The magnetic properties of fractal structures”

Mercoledì 13 Aprile 2022, ore 17:30 - Zoom - Maria Rosaria Lancia (Università degli Studi di Roma “La Sapienza”)


Trying to understand the magnetic properties of fractal structures is a new challenge from both the practical and theoretical point of view. In this talk, I present some results for a magnetostatic problem in a 3D “cylindrical” domain of Koch type and in its corresponding prefractal approximating domains. Crucial tools, to prove well-posedness results, are a generalized Stokes formula and the Friedrichs inequality for domains with fractal boundary. We investigate the convergence of the pre-fractal solutions to the limit fractal one. We also consider the numerical approximation of the pre-fractal problems via FEM and we give a priori error estimates. Some numerical simulations are also shown.

This is joint work with S. Creo (Sapienza, Università di Roma), M. Hinz (Bielefeld University), A. Teplyaev (University of Connecticut).

Online Seminar on Mathematical Methods in the Theory of Electromagnetism