**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.**