Trace Theorems on Non-Smooth Boundaries for Functional Spaces Related to Maxwell Equations: an Overview

摘要

We study tangential vector fields on the boundary of a bounded Lip-schitz domain in R~3. Our attention is focused on the definition of suitable Hilbert spaces over a range of Sobolev regularity which we try to make as large as possible, and also on the construction of tangential differential operators. Hodge decompositions are proved to hold for some special choices of spaces which are of interest in the theory of Maxwell equations.