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PDE Seminar

Speaker: Abner J. Salgado


Title: The Bogovskii and regularized Poincare integral operators


Abstract: A fundamental result in the analysis of incompressible models of fluids
is the existence of a right inverse of the divergence. This, in
particular, implies the validity of a Korn inequality, which is an
important tool in the theory of elasticity. In 1979 M.E. Bogovskii
provided an explicit construction of such inverse, via a singular
integral operator.

Vector fields and the operators of vector calculus are particular cases
of differential forms on a manifold, the exterior derivative, and its
properties. It is then natural to pose the question about the existence
of the right inverse of the exterior derivative or, in the language of
differential forms, to find conditions that guarantee that a closed
form is exact. In the classical setting this is accomplished by the so-
called "Cartan's magic formula", a sort of path integral.

In this talk we consider the extension of these two results to
differential forms valued in Sobolev spaces, and closely examine the
dependence of the continuity constants for these operators on certain
geometric characteristics of the domain.

This is joint work with Johnny Guzman (Brown University)

Thursday, October 22, 2020 at 2:50pm to 4:00pm

Virtual Event
Event Type

Lectures & Presentations, Meetings & Conferences




General Public



Contact Name

Tuoc Phan

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