Event
01_1
| 제출번호(No.) | 0145 |
|---|---|
| 분류(Section) | Special Invited Lecture |
| 분과(Session) | Analysis (AN) |
| 영문제목 (Title(Eng.)) |
On the Hardy-Sobolev type elliptic equations with multiple boundary singularities and Caffarelli-Kohn-Nirenberg inequality |
| 저자(Author(s)) |
Jann-Long Chern 1 National Central University1 |
| 초록본문(Abstract) | In this talk we are interested in how the geometry of boundary singularities can affect the existence of positive solutions of elliptic equations. In particular, we study the Dirichlet problem for an elliptic equation with multiple singularities on the boundary of a domain. In many nice results, the conditions on curvature approach have been extensively explored in several different cases to study the existence of positive solutions of such kind problems. In this talk we propose a more general criterion to study the existence result by the concept of contact order. This new contact order approach provides a refined way to analyze boundary singularities, and includes the curvature approach as a special case. A novel feature here is that we are able to obtain positive results for convex domains such as a ball, a half sphere or a rectangular box which are unreachable by the standard curvature method. Our second theorem is a non-existence result which suggests that our previous existence result is optimal for certain convex domains. This type of optimality is rarely addressed in literature. In the third part of this talk, we generalize the above theorems to $N=3$ and show the existence of minimizers for the Caffarelli-Kohn-Nirenberg inequalities when $N=3$--this solves the problem left open in [Chern and Lin, 2010 ARMA], hence completing a long line of research. This talk are based on the joint works with X. Fang and C. Hsia, and C.-S. Lin respectively. |
| 분류기호 (MSC number(s)) |
35J20 (47J30, 49K10) |
| 키워드(Keyword(s)) | boundary singularity; Hardy-Sobolev; Caffarelli-Kohn-Nirenberg inequality |
| 강연 형태 (Language of Session (Talk)) |
English |