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Curvature flows with a flat side : 평평한 측면이 있는 곡률 흐름

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Authors
장효석
Advisor
이기암
Issue Date
2020
Publisher
서울대학교 대학원
Keywords
35A01 Existence problems for PDEs35K65 Degenerate parabolic equations35R35 Free boundary problems for PDEs53C44 Geometric evolution equations35A01 PDE존재성문제35K65 퇴화포물형방정식35R35 PDE자유경계문제53C44 기하발전방정식
Description
학위논문 (박사) -- 서울대학교 대학원 : 자연과학대학 수리과학부, 2020. 8. 이기암.
Abstract
We study the near-the-interface behavior of a compact convex scalar curvature flow with a flat side. Under suitable initial conditions on the flat side, we show that the interface propagates with a finite and non-degenerate speed and the level set with a finite speed, until the flat side vanishes. Then we get optimal derivative estimates of the pressure-like function, non-degeneracy of the speed of the level set, optimal decay estimates of curvatures near the interface, and a generalized version of Kim-Lee-Rhees curvature lower bound, from which we obtain the Hölder regularity of the ratio of the curvature to the optimal decay rate up to the free boundary. In the end, we demonstrate the all-time existence of a solution which is smooth up to the interface in its support.
Language
eng
URI
https://hdl.handle.net/10371/170697

http://dcollection.snu.ac.kr/common/orgView/000000162723
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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