Elliptic equations with singular drifts term on Lipschitz domains.

Abstract: In this talk, we consider linear elliptic equation of second-order with the first term given by a singular vector field $\mathbf{b}$ on bounded Lipschitz domains $\Omega$ in $\mathbb{R}^n$, $(n\geq 3)$. Under the assumption $\mathbf{b}\in L^n(\Omega)^n$, we establish unique solvability in $L_{\alpha}^p(\Omega)$ for Dirichlet and Neumann problems. Here $L_{\alpha}^p(\Omega)$ denotes the standard Sobolev spaces(or Bessel potential space) with the pair $(\alpha,p)$ satisfying certain condition. These results extend the classical works of Jerison-Kenig (1995) and Fabes-Mendez-Mitrea (1999) for the Poisson equation. In addition, we study the Dirichlet problem for such linear elliptic equation when the boundary data is in $L^2(\partial\Omega)$. Necessary review on this topics is also presented in this talk. This is a joint work with Hyunseok Kim(Sogang University).

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.