The Dirichlet problem for weakly harmonic maps with rough data

Abstract: In this talk, we will discuss the well-posedness issues for weakly harmonic maps subject to Dirichlet boundary data assuming a minimal regularity. After a brief description of the problem we will present our techniques which partly rely on certain fundamental notions in harmonic analysis such as Carleson measures, its intrinsic connection to the John-Nirenberg space BMO and the Laplace operator... With an appropriate reformulation of our problem, various solvability results (existence, uniqueness and regularity) will then be reviewed. Our approach (nonvariational), as we will see, is suitable for the analysis of critical or endpoint elliptic boundary value problems and hence can unambiguously be applicable to similar type of equations or systems driven by classical operators. For this talk, we only mention a generalization of our results to second-order constant elliptic systems.

This is a joint work with Herbert Koch.

analysis of PDEsclassical analysis and ODEs

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.