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UID:c30aaab6ca53b3940c9eb13450f9a283
CATEGORIES:Nonlinear Analysis
CREATED:20221205T124114
SUMMARY:Regularity for some fully nonlinear equations in conformal geometry
LOCATION:Hill Center Room 705
DESCRIPTION:Abstract: The sigma_k Yamabe problem is a fully nonlinear generalisation of
  the Yamabe problem, in which one looks to prescribe symmetric functions of
  the eigenvalues of the Schouten tensor to be constant within a fixed confo
 rmal class. In the last 20 years or so, there has been a significant amount
  of progress on the sigma_k Yamabe problem in the so-called positive case, 
 leading to many existence results for smooth solutions. In this talk, I wil
 l discuss some recent results on the regularity theory for the sigma_k Yama
 be equation, with an emphasis on W^{2,p} solutions in both the positive and
  negative cases, and viscosity solutions to the degenerate problem. I will 
 also mention some open problems in the field. Much of the talk will be base
 d on joint work with Luc Nguyen.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Abstract: The sigma_k Yamabe problem is a fully nonlinear generalisation
  of the Yamabe problem, in which one looks to prescribe symmetric functions
  of the eigenvalues of the Schouten tensor to be constant within a fixed co
 nformal class. In the last 20 years or so, there has been a significant amo
 unt of progress on the sigma_k Yamabe problem in the so-called positive cas
 e, leading to many existence results for smooth solutions. In this talk, I 
 will discuss some recent results on the regularity theory for the sigma_k Y
 amabe equation, with an emphasis on W^{2,p} solutions in both the positive 
 and negative cases, and viscosity solutions to the degenerate problem. I wi
 ll also mention some open problems in the field. Much of the talk will be b
 ased on joint work with Luc Nguyen.</p>
CONTACT:Jonah Duncan, Johns Hopkins University
DTSTAMP:20260827T043219
DTSTART;TZID=America/New_York:20221213T134000
DTEND;TZID=America/New_York:20221213T144000
SEQUENCE:0
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