Conference abstracts

Session C4 - Foundations of Numerical PDEs

July 19, 15:00 ~ 15:25 - Room B6

Weights and applications in numerics

Abner J Salgado

University of Tennessee, USA   -   asalgad1@utk.edu

The use of weights and weighted norm inequalities has a rich history in harmonic analysis and the study of regularity properties to solutions of partial differential equations (PDE). Starting from classical results, we will present an overview of the application of some of these ideas to the numerical analysis of PDEs. Our main attention will be on some recent results concerning the use of weights in fractional diffusion, problems with singular data and PDE constrained optimization problems. Although these seem as disparate and unrelated applications, it is remarkable that the only structural assumption on the weight is that it belongs to a so-called Muckenhoupt $A_p$ class, which has been thorougly studied in harmonic analysis since the 1970's.

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