The Regularity boundary value problem in domains with lower dimensional boundaries.

Abstract: Recently, Guy David, Joseph Feneuil and Svitlana Mayboroda developed an elliptic theory in domains with lower dimensional boundaries. They studied a class of degenerate second order elliptic operators $-\textup{div} A\nabla$ , where A is a weighted matrix. The Dirichlet boundary value problem associated with these operators in higher codimension has already been solved by Joseph Feneuil, Svitlana Mayboroda and Zihui Zhao. We currently focus on the regularity boundary problem. Roughly speaking, we are interested in the relation between the gradient of weak solutions and the gradient of boundary data whenever the boundary has higher regularity and coefficients satisfy a certain smoothness condition . In this talk, I will introduce our main results about the solvability of the regularity boundary value problem in the higher codimension. This is joint work with Svitlana Mayboroda and Joseph Feneuil.

analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.