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UID:59ac7c0597782dbb407301038630c355
CATEGORIES:Nonlinear Analysis
CREATED:20230923T123738
SUMMARY:A doubling approach for sigma-k PDEs
LOCATION:Hill 705
DESCRIPTION:<p style="font-weight: 400; letter-spacing: normal; text-indent: 0px; text-
 transform: none; white-space: normal; word-spacing: 0px; text-decoration: n
 one; color: #000000; text-align: left;"><strong>Abstract:&nbsp;</strong>The
  interior regularity for viscosity solutions of the sigma-2 equation is the
  remaining case of the Monge-Ampere sigma-k family to be understood. The di
 mension two case was done in the 1950’s by Heinz, and the dimension three c
 ase was done in 2008 by Warren and Yuan. In joint works with Yu Yuan, we sh
 ow regularity in dimension four for sigma-2. Our argument uses a doubling i
 nequality for the Hessian. A similar argument gives a proof of interior reg
 ularity for strictly convex solutions of the Monge-Ampere (sigma-n) equatio
 n in all dimensions, using a geometric approach distinct from Pogorelov’s m
 aximum principle of the 70’s.</p>
CONTACT:Ravi Shankar, Princeton University
DTSTAMP:20260908T221457
DTSTART;TZID=America/New_York:20230926T134000
DTEND;TZID=America/New_York:20230926T144000
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