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UID:20250709T123613EDT-0913su2VfW@132.216.98.100
DTSTAMP:20250709T163613Z
DESCRIPTION:Title: Uniform rectifiability and elliptic operators satisfying
  a Carleson measure condition.\n\n\n	Abstract: In this talk I will study th
 e correspondence between the properties of the solutions of a class of PDE
 s and the geometry of sets in Euclidean space. We settle the question of w
 hether (quantitative) absolute continuity of the elliptic measure with res
 pect to the surface measure and uniform rectifiability of the boundary are
  equivalent\, in an optimal class of divergence form elliptic operators sa
 tisfying a suitable Carleson measure condition. Our setting is that of dom
 ains having an Ahlfors regular boundary and satisfying the so-called inter
 ior Corkscrew and Harnack chain conditions (these are respectively scale-i
 nvariant/quantitative versions of openness and path-connectivity) and we s
 how that for the class of Kenig-Pipher uniformly elliptic operators (opera
 tors whose coefficients have controlled oscillation in terms of a Carleson
  measure condition) the solvability of the $L^p$-Dirichlet problem with so
 me finite $p$ is equivalent to the quantitative openness of the exterior d
 omains or to the uniform rectifiablity of the boundary. Joint work with S.
  Hofmann\, S. Mayboroda\, T. Toro\, and Z. Zhao.\n\n \n\nFor Zoom meeting 
 information please contact dmitry.jakobson [at] mcgill.ca\n
DTSTART:20200911T130000Z
DTEND:20200911T140000Z
SUMMARY:Jose Maria Martell (ICMAT)
URL:/mathstat/channels/event/jose-maria-martell-icmat-
 324340
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