“Regularity theory for Maxwell’s equations”
Mercoledì 13 Gennaio 2021, ore 17:00 - Zoom - Giovanni Alberti (Università di Genova)
In this talk, we will review the main results regarding the regularity properties of the solutions to time-harmonic Maxwell’s equations. The main tool is the Helmholtz decomposition of the electric and magnetic fields, which allows us to reduce Maxwell’s equations to a system of elliptic equations for the scalar and vector potentials. The regularity of the potentials then follows by classical elliptic regularity theory. We will discuss regularity in Sobolev and Hölder spaces, and consider interior as well as boundary estimates (in smooth domains).