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SUMMARY:Juncheng Wei (University of British Colombia)
DTSTART:20210120T143000Z
DTEND:20210120T153000Z
DTSTAMP:20260423T024622Z
UID:NCTS-GMT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCTS-GMT/2/"
 >Second order estimates for interfaces of Allen-Cahn</a>\nby Juncheng Wei 
 (University of British Colombia) as part of NCTS international Geometric M
 easure Theory seminar\n\n\nAbstract\nIn this talk I will discuss a uniform
  $C^{2\,\\theta}$ estimate for level sets of stable solutions to the singu
 larly perturbed Allen-Cahn equation in dimensions $n \\leq 10$ (which is o
 ptimal). The proof combines two ingredients: one is a reverse application 
 of the infinite dimensional Lyapunov-Schmidt reduction method which enable
 s us to reduce the $C^{2\,\\theta}$ estimate for these level sets to a cor
 responding one on solutions of Toda system\; the other one uses a small re
 gularity theorem on stable solutions of Toda system to establish various d
 ecay estimates\, which gives a lower bound on distances between different 
 sheets of solutions to Toda system or level sets of solutions to Allen-Cah
 n equation. (Joint work with Kelei Wang.)\n
LOCATION:https://researchseminars.org/talk/NCTS-GMT/2/
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