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SUMMARY:Moritz Egert (Université Paris-Sud (Orsay))
DTSTART:20210419T160000Z
DTEND:20210419T165000Z
DTSTAMP:20260423T024837Z
UID:anpdews/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/59/"
 >Boundary value problems for elliptic systems with block structure</a>\nby
  Moritz Egert (Université Paris-Sud (Orsay)) as part of HA-GMT-PDE Semina
 r\n\n\nAbstract\nI’ll consider a very simple elliptic PDE in the upper h
 alf-space: divergence form\, transversally independent coefficients and no
  mixed transversal-tangential derivatives. In this case\, the Dirichlet pr
 oblem can formally be solved via a Poisson semigroup\, but there might not
  be a heat semigroup. The construction is rigorous for L2 data. For other 
 data classes X (Lebesgue\, Hardy\, Sobolev\, Besov\,…) the question\, wh
 ether the corresponding Dirichlet problem is well-posed\, is inseparably t
 ied to the question\, whether there is a compatible Poisson semigroup on X
 . \n\n\nOn a "semigroup space" the infinitesimal generator has (almost?) e
 very operator theoretic property that one can dream of and these can be us
 ed to prove well-posedness. But it turns out that there are genuinely more
  "well-posedness spaces" than "semigroup spaces". For example\, up to boun
 dary dimension n=4 there is a well-posed BMO-Dirichlet problem\, whose uni
 que solution has no reason to keep its tangential regularity in the interi
 or of the domain. \n\n\nI’ll give an introduction to the general theme a
 nd discuss some new results\, all based on a recent monograph jointly writ
 ten with Pascal Auscher.\n
LOCATION:https://researchseminars.org/talk/anpdews/59/
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