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SUMMARY:Lewy's Example - Conor Heffernan
DTSTART:20180315T153000Z
DTEND:20180315T163000Z
UID:TALK103036@talks.cam.ac.uk
CONTACT:Kasia Wyczesany
DESCRIPTION:During ‘Analysis of PDEs’ in Michaelmas term we proved the
  Cauchy-Kovalevskaya theorem. The theorem asserts the local existence of a
  solution for a certain class of first order systems of PDEs. The hypothes
 is of the theorem requires all given functions within the system are analy
 tic. The analyticicty is a key component of the hypothesis as the celebrat
 ed example due to Lewy shows that smoothness is not enough to guarantee th
 ese systems have solutions. This is done by construction of a linear PDE w
 hich has no solutions at all. In this talk\, a statement of the Cauchy-Kov
 alevskaya theorem will be given and the statement of Lewy’s example and 
 a proof (or at least a sketch\, depending on time) that the example is in 
 fact a PDE with no solutions will also be given.
LOCATION:MR11
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