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SUMMARY:Computing lower eigenvalues on rough domains - Lyonell Boulton (He
 riot-Watt University)
DTSTART:20240222T150000Z
DTEND:20240222T160000Z
UID:TALK210130@talks.cam.ac.uk
CONTACT:Nicolas Boulle
DESCRIPTION:In this talk I will describe a strategy for finding sharp uppe
 r and lower numerical bounds of the Poincare constant on a class of planar
  domains with piecewise self-similar boundary. The approach is developed i
 n [A] and it consists of four main blocks: 1) tight inner-outer shape inte
 rpolation\, 2) conformal mapping of the approximate polygonal regions\, 3)
  grad-div system formulation of the spectral problem and 4) computation of
  the eigenvalue bounds. After describing the method\, justifying its valid
 ity and reporting on general convergence estimates\, I will show concrete 
 evidence of its effectiveness on the Koch snowflake. I will conclude the t
 alk by discussing potential applications to other linear operators on roug
 h regions. This research has been conducted jointly with Lehel Banjai (Her
 iot-Watt University).\n\n[A] J. Fractal Geometry 8 (2021) No. 2\, pp. 153-
 188
LOCATION:Centre for Mathematical Sciences\, MR14
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