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SUMMARY:Ryan Alvarado (Amherst College)
DTSTART:20200908T170000Z
DTEND:20200908T180000Z
DTSTAMP:20260423T021012Z
UID:OSGA/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/27/">A 
 characterization of the Sobolev embedding theorem in metric-measure spaces
 .</a>\nby Ryan Alvarado (Amherst College) as part of Online Seminar "Geome
 tric Analysis"\n\n\nAbstract\nHistorically\, the Sobolev embedding theorem
  on domains has played a key role in establishing many fundamental results
  in the area of analysis and it is well known that the geometry of the und
 erlying domain is intimately linked to the availability of these embedding
 s. In fact\, certain geometrical characterizations of domains which suppor
 t Sobolev embeddings have been obtained in the Euclidean setting. In this 
 talk\, we will revisit these embedding theorems in the more general contex
 t of metric-measure spaces and discuss some recent work which identifies a
  measure theoretic condition that is both necessary and sufficient to ensu
 re their veracity. A measure characterization of Sobolev extension domains
  in the metric setting as well as applications of our methods to spaces su
 pporting $p$-Poincaré inequalities will also be discussed. This talk is b
 ased on joint work with Przemysław Górka (Warsaw University of Technolog
 y)\, Piotr Hajłasz (University of Pittsburgh).\n
LOCATION:https://researchseminars.org/talk/OSGA/27/
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