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SUMMARY:José Luis Luna García (University of Missouri)
DTSTART:20200727T150000Z
DTEND:20200727T155000Z
DTSTAMP:20260423T024836Z
UID:anpdews/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/16/"
 >Critical Perturbations for Linear Elliptic Equations</a>\nby José Luis L
 una García (University of Missouri) as part of HA-GMT-PDE Seminar\n\n\nAb
 stract\nIn this talk we develop a perturbation theory for the L^2 solvabil
 ity of certain Boundary Value Problems for linear elliptic equations with 
 complex coefficients in the upper half space. While we expect the methods 
 to apply to general systems and higher order equations\, we will focus her
 e on the general scalar second order equation\, for which most of the main
  difficulties are already present: For instance a lack of boundedness and 
 continuity of solutions\, precluding the use of a pointwise-defined fundam
 ental solution.\n\nOur theory is based on solvability via the method of la
 yer potentials. As such the main points to consider are boundedness and in
 vertibility\, in the appropriate functional spaces\, of the corresponding 
 operators and their boundary traces. For the boundedness issue we employ t
 he theory of local Tb theorems\, to obtain control on certain square funct
 ions that allow us to conclude the desired bounds on the layer potentials.
  The invertibility  will be treated through the analyticity of the boundar
 y traces as a function of the coefficients of the equation.\n\nOf technica
 l interest is that our methods allow us to obtain nontangential maximal fu
 nction estimates for the layer potential solutions so constructed.\n\nThis
  is joint work with Simon Bortz\, Steve Hofmann\, Svitlana Mayboroda\, and
  Bruno Poggi.\n
LOCATION:https://researchseminars.org/talk/anpdews/16/
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