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SUMMARY:Computing eigenvalues of the Laplacian on rough domains - Alexei S
 tepanenko
DTSTART:20230622T143000Z
DTEND:20230622T153000Z
UID:TALK202681@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:In this talk\, I shall present a joint work with Frank Rösler
  in which we consider the computability of eigenvalues of the Dirichlet La
 placian on bounded domains with rough\, possibly fractal\, boundaries. We 
 work within the framework of Solvability Complexity Indices\, which allows
  us to formulate the problem rigorously. On one hand\, we construct an alg
 orithm that provably converges for any domain satisfying a collection of m
 ild topological hypotheses\, on the other\, we prove that there does not e
 xist an algorithm of the same type which converges for an arbitrary bounde
 d domain. Along the way\, we develop new spectral convergence results for 
 the Dirichlet Laplacian on rough domains\, as well as a novel Poincaré-ty
 pe inequality.
LOCATION:Centre for Mathematical Sciences\, MR14
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