BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.15.17.1//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Claremont Center for the Mathematical Sciences
X-ORIGINAL-URL:https://colleges.claremont.edu/ccms
X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:America/Los_Angeles
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20250309T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20251102T090000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20260308T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20261101T090000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20270314T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20271107T090000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260413T161500
DTEND;TZID=America/Los_Angeles:20260413T171500
DTSTAMP:20260415T172036
CREATED:20260320T224421Z
LAST-MODIFIED:20260320T224421Z
UID:4058-1776096900-1776100500@colleges.claremont.edu
SUMMARY:Extremal Eigenvalues of Weighted Steklov Problems (Chiu-Yen Kao\, CMC)
DESCRIPTION:Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are bang-bang functions and may have disconnected support\, while maximizers are not necessarily bang-bang. On circular domains\, the minimization problem admits infinitely many minimizers generated by rotational symmetry\, while the maximization problem has infinitely many distinct maximizers that are not symmetry-induced. We also show that an eigenvalue is generally neither convex nor concave with respect to the density function\, limiting the use of classical convex optimization tools. To address these challenges\, we analyze the objective functional and introduce a Fréchet differentiable surrogate that enables the derivation of optimality conditions. We further design an efficient numerical algorithm\, with experiments illustrating the difficulty of recovering optimal densities when they lack smoothness or exhibit oscillations.
URL:https://colleges.claremont.edu/ccms/event/extremal-eigenvalues-of-weighted-steklov-problems-chiu-yen-kao-cmc/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
END:VEVENT
END:VCALENDAR