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CATEGORIES:Lectures & Presentations,Meetings & Conferences
DESCRIPTION:Speaker: Abner J. Salgado \n\n \n\nTitle: The Bogovskii and reg
ularized Poincare integral operators\n\n \n\nAbstract: A fundamental result
in the analysis of incompressible models of fluidsis the existence of a ri
ght inverse of the divergence. This\, inparticular\, implies the validity o
f a Korn inequality\, which is animportant tool in the theory of elasticity
. In 1979 M.E. Bogovskiiprovided an explicit construction of such inverse\,
via a singularintegral operator.Vector fields and the operators of vector
calculus are particular casesof differential forms on a manifold\, the exte
rior derivative\, and itsproperties. It is then natural to pose the questio
n about the existenceof the right inverse of the exterior derivative or\, i
n the language ofdifferential forms\, to find conditions that guarantee tha
t a closedform is exact. In the classical setting this is accomplished by t
he so-called "Cartan's magic formula"\, a sort of path integral.In this tal
k we consider the extension of these two results todifferential forms value
d in Sobolev spaces\, and closely examine thedependence of the continuity c
onstants for these operators on certaingeometric characteristics of the dom
ain.This is joint work with Johnny Guzman (Brown University)
DTEND:20201022T200000Z
DTSTAMP:20210124T173844Z
DTSTART:20201022T185000Z
LOCATION:
SEQUENCE:0
SUMMARY:PDE Seminar
UID:tag:localist.com\,2008:EventInstance_34839089613694
URL:https://calendar.utk.edu/event/pde_seminar_8168
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