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SUMMARY:Regularity of Lipschitz Solutions to the Minimal Surface Equation 
 - Spencer Hughes (University of Cambridge)
DTSTART:20111116T160000Z
DTEND:20111116T173000Z
UID:TALK32796@talks.cam.ac.uk
CONTACT:Damon Civin
DESCRIPTION:It is well-known that a Lipschitz weak solution of the Minimal
  Surface Equation (MSE) is smooth in the interior of the domain. Usually\,
  a lot of work (called De Giorgi-Nash-Moser Theory) goes into establishing
  the Holder continuity of the first derivatives\, after which general prin
 ciples from the theory of linear PDE take over and guarantee smoothness. \
 n\nDrawing inspiration from techniques in geometric measure theory\, one i
 s able to\, in the case of the MSE\, devise an alternative approach to est
 ablishing the Holder continuity of the first derivatives which is complete
 ly expressible in the language of PDE but which avoids De Giorgi-Nash-Mose
 r theory. I will outline this method\, focussing on the geometry of the te
 chniques.
LOCATION:MR14\, CMS
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