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學術演講

Analysis Seminar

Complete rigidity at infinity and existence of the Levinson cavity

2026/10/20 (Tue.) 10:00~13:00
  • 日期 : 2026/10/20 (Tue.) 10:00~13:00
  • 地點 : online
  • 主講人 : Chunjing Xie (Shanghai Jiao Tong University)
  • 籌辦人 : Tai-Ping Liu (AS)
  • 演講摘要 : In 1946, assuming a power-law ansatz with a slowly varying correction for asymptotic shape, Norman Levinson derived a precise asymptotic formula for axially symmetric cavities. However, his result requires very strong assumptions such that it has remained an open problem whether the cavity solutions, which we know to exist by Garabedian-Lewy-Schiffer and Caffarelli-Friedman, actually share this asymptotic behavior, or whether at least one solution possessing the Levinson asymptotics exists. We present a potential theoretic approach, which reduces the analysis of the asymptotic shape of free surfaces to the analysis of a precise ordinary differential equation. The approach relies mainly on the principal part of the PDE operator to allow for a representation formula and is thus not restricted to problems of elliptic type. With the aid of this approach, we obtain complete rigidity at infinity of the Levinson solution in the class of axially symmetric solutions, that is, any solution satisfying mild and natural assumptions at the fixed boundary and infinity converges asymptotically to the Levinson profile.

Click here to register: https://forms.gle/aYBBzmUwbEWkmBMW6  (Deadline: 4pm, Oct. 19)
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請注意截止時間，逾時不受理報名。Please note the deadline; no applications will be accepted after the deadline.

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