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Lectura de tesis
ANÁLISIS ARMÓNICO EN
DOMINIOS IRREGULARES
PHD STUDENT: Juan Cavero de Carondelet (ICMAT)
ADVISOR: José María Martell (ICMAT)
DATE: Friday, 24 May 2019 - 12:00
VENUE: Aula Naranja, ICMAT
ABSTRACT: We study the problem of perturbation of elliptic operators in rough
domains. Given two operators L0 = ‒ div(A0∇.) and L = ‒ div(A∇.), we look for
conditions in the discrepancy between A0 and A that allow us to transfer good
properties from one operator to the other. For instance, we are interested in the
fact that their elliptic measures belong to the class A∞. We extend the result of
Fefferman-Kenig-Pipher to 1-sided CAD domains. This is, assuming a Carleson
measure condition in the discrepancy between both matrices, we show that one
of the elliptic measures belongs to A∞ if the same property holds for the other.
To prove this result we will present two independent methods that are different
from the one used by Fefferman-Kenig-Pipher. The first method uses the
“bootstrapping of Carleson measures” technique, and it requires to consider
the “small perturbation” case. The second method is a new approach that relies
on the property that every bounded weak solution of a given operator satisfy
Carleson measure estimates.