Dirichlet problem and regular boundary points for elliptic equations in non-divergence and double divergence form
bk21
129동 101호
0
1372
03.06 13:17
| 구분 | Rookies Pitch |
|---|---|
| 일정 | 2026-03-19(목) 16:00~16:30 |
| 세미나실 | 129동 101호 |
| 강연자 | 김동하 (서울대학교) |
| 담당교수 | 서인석 |
| 기타 |
In the theory of elliptic partial differential equations, the Dirichlet problem has long been a central topic. A fundamental question is to identify domains for which the Dirichlet problem is always solvable.
Equivalently, this question leads to the characterization of regular boundary points, a classical problem in the theory of elliptic equations.. For the Laplace equation, this problem was completely solved by Wiener in 1924. He established the celebrated Wiener criterion, which characterizes regular boundary points in terms of a series of capacities.
In this talk, we consider the Dirichlet problem for second-order elliptic equations in non-divergence form and double divergence form. We introduce a potential theory framework for these operators, including Perron’s method, capacity theory, and Wiener’s criterion.
Assuming that the leading coefficients satisfy the Dini mean oscillation condition, we also establish the equivalence between regular boundary points for these operators and those for the Laplace operator.
