Abstract:

The regularized Poincare' integral operators are a new tool in the
analysis of differential forms that have a variety of different
applications. In particular, they allow the construction of vector
and scalar potentials of optimal regularity
  in terms of fractional order Sobolev norms. They also have useful
mapping properties in polynomial spaces that are
  related to discrete differential forms. One recent application is
the completion of the proof of the discrete compactness
  of the p version of edge elements approximation of the Maxwell
eigenvalue problem.

In the talk, these integral operators and their companions, the
Bogovskii integral operators, are presented with their main
properties. Their role for the p version edge element approximation
of the Maxwell eigenproblem is explained.