SEMINARIO DE ANÁLISIS Y APLICACIONES

Jueves, 8 de mayo de 2025,
15:30 - 16:30, Aula 520, departamento de Matemáticas

Jill Pipher
Brown University

The Regularity problem for a class of parabolic divergence form equations

Resumen:
In recent joint work with M. Dindos and L. Li, we show that the Regularity problem for a
class of second order divergence form parabolic operators is solvable when the data
belongs to an appropriate Lp space. The parabolic operators have coefficients that
vary in both space and time, and satisfy a certain minimal smoothness assumption
defined by a Carleson measure condition - one that has been well-studied for the
elliptic analog of these equations. The long term goal, of which this is a step, is to
bring the parabolic theory to the level of understanding that has now been achieved
for elliptic boundary value problems and beyond to free boundary problems.