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X-WR-CALNAME:Math Colloquia
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BEGIN:VEVENT
DTSTART:20211008T210000Z
UID:158432@events.unl.edu
DTSTAMP:20210807T143133Z
ORGANIZER;CN=Petronela Radu:MAILTO:pradu@unl.edu
SUMMARY:Marta Lewicka\, University of Pittsburgh
STATUS:CONFIRMED
DESCRIPTION:The following approach of finding solutions to a partial differ
ential equation Lu=0\, proved to be quite versatile\:\n\n(i) develop an as
ymptotic expansion of a suitable family of averaging operators on u\; the
operators are parametrized by the radius \epsilon of averaging\;\n\n(ii) s
tudy the related mean value equation by removing higher order terms in the
expansion\;\n\n(iii) interpret the mean value equation as the dynamic pro
gramming principle of a two-player game incorporating deterministic and st
ochastic components\;\n\n(iv) pass to the limit in the radius of averaging
\epsilon\, in order to recover solutions to Lu=0 from the values of the g
ame process.\n\nIn my talk\, I will explain this approach in the following
contexts\: p-Laplacian\; non-local geometric p-Laplacian\; Robin boundary
conditions\; and weighted Laplace-Beltrami operator on a manifold. In eac
h case\, finding the appropriate averaging principle and the related game\
, is the key starting point.
LOCATION:Avery Hall Room
URL://events.unl.edu/math-colloquia/2021/10/08/158432/
DTEND:20211008T215000Z
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