BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:PDE / Analysis Seminar 
X-WR-TIMEZONE:Eastern Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260518T054341Z
UID:tag:localist.com\,2008:EventInstance_32546478178398
DTSTART:20200225T200000Z
DTEND:20200225T220000Z
DESCRIPTION:3pm\n\nFeatured Speaker :  Svitlana Mayboroda (U Minnesota)\n\n
 Title :  Rectifiability is necessary and sufficient\n\nAbstract : \n\nWe s
 hall discuss optimal conditions on the geometry of the domain responsible 
 for solvability of the Dirichlet problem\, or absolute continuity of the h
 armonic measure with respect to the Lebesgue measure. In rough terms\, the
  question is: do Brownian travelers see pieces of the boundary of the doma
 in according to their Lebesgue size\, or\, if not\, what do they see? In 1
 916 F. and M. Riesz proved that in a simply connected planar domain rectif
 iability is sufficient\, and over the years this result has been extended 
 to higher dimensions. The centerpoint of our discussion will be a recently
  proved converse to F. & M. Riesz’ theorem: rectifiability is also neces
 sary for the absolute continuity of the harmonic measure with respect to t
 he Lebesgue measure for n−1 dimensional sets in Rn . We shall also touch
  upon a more general setting of domains with lower dimensional boundaries.
 \n\n4pm\n\nFeatured Speaker :  Patricia Ruiz (Texas A&M)\n\nTitle :  Morre
 y's inequality in Dirichlet spaces\n\nAbstract : \n\nMorrey’s inequality
  in R n is a classical Sobolev embedding that has many important applicati
 ons\, for instance in the regularity theory of elliptic PDEs. Roughly spea
 king\, this inequality asserts that functions in the Sobolev space W1\,p(R
  n ) are H¨older continuous for any n < p < ∞ with an explicit optimal 
 exponent that depends on n and p. In this talk we will present Morrey’s 
 inequality in the more general framework of Dirichlet spaces with (sub-)Ga
 ussian heat kernel estimates. In particular\, we will discover that the op
 timal exponent not only depends on the Hausdorff and the walk dimension\, 
 but also on a further invariant of the space. To this end\, we will discus
 s a recent approach to (1\, p)- Sobolev spaces via heat semigroups inspire
 d by ideas that go back to work of de Giorgi and Ledoux. If time permits\,
  we will outline some results and conjectures concerning a critical expone
 nt which might be related to other dimensions of interest in the theory of
  metric measure spaces. This talk is based on joint work with F. Baudoin.
GEO:42.358825;-71.090029
LOCATION:2-361\, 2-361
SUMMARY:PDE / Analysis Seminar 
URL;VALUE=URI:https://calendar.mit.edu/event/pde_analysis_seminar_1783
CATEGORIES:Conferences/Seminars/Lectures
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