| [18.03.06] 수학과 콜로퀴움 | |||||
| 작성자 | 하** | 작성일 | 2018-03-07 | 조회수 | 365 |
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수학과 강연회 1. 강연자 : Kanishka 2. 소속 : Florida Institute of Technology 3. 강연일시 : 3월 6일 (화) 5시 4. 장소 : 8- 412 호 5. 제목 : Higher Critical Points in an Elliptic Free Boundary Problem 6. 초록 : We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied extensively. But because the functionals are not smooth, standard variational methods cannot be used directly to prove the existence of higher critical points. Here we find a nontrivial critical point of mountain pass type and prove many of the same estimates known for minimizers, including Lipschitz continuity and nondegeneracy. We then show that the free boundary is smooth in dimension 2 and prove partial regularity in higher dimensions |
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