A New Elliptic Measure on Lower Dimensional Sets |
| |
Authors: | Guy David Joseph Feneuil Svitlana Mayboroda |
| |
Institution: | 1. Université Paris-Sud, Laboratoire de Mathématiques, UMR8628, Orsay, F-91405, France;
2. Department of Mathematics, Temple University, Philadelphia, PA 19122, USA;
3. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA |
| |
Abstract: | The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of n-1 dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys the first steps of a program recently launched by the authors and aimed at the new PDE approach to sets with lower dimensional boundaries. We define a suitable class of degenerate elliptic operators, explain our intuition, motivation, and goals, and present the first results regarding absolute continuity of the emerging elliptic measure with respect to the surface measure analogous to the classical theorems of C. Kenig and his collaborators in the case of co-dimension one. |
| |
Keywords: | Elliptic measure in higher codimension degenerate elliptic operators absolute continuity Dahlberg's theorem Dirichlet solvability |
本文献已被 CNKI SpringerLink 等数据库收录! |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学学报(英文版)》下载免费的PDF全文 |
|