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UID:20251019T005501EDT-5098bJRbVe@132.216.98.100
DTSTAMP:20251019T045501Z
DESCRIPTION:Title: Concavity of solutions to elliptic equations on the sphe
 re\n	Abstract: An important question in PDE is when a solution to an ellipt
 ic equation is concave. This has been of interest with respect to the spec
 trum of linear equations as well as in nonlinear problems. An old techniqu
 e going back to works of Korevaar\, Kennington and Kawohl is to study a ce
 rtain two-point function on a Euclidean domain to prove a so-called concav
 ity maximum principle with the help of a first and second derivative test.
 \n	To our knowledge\, so far this technique has never been transferred to o
 ther ambient spaces\, as the nonlinearity of a general ambient space intro
 duces geometric terms into the classical calculation\, which in general do
  not carry a sign.\n	In this talk we have a look at this situation on the u
 nit sphere. We prove a concavity maximum principle for a broad class of de
 generate elliptic equations via a careful analysis of the spherical Jacobi
  fields and their derivatives. In turn we obtain concavity of solutions to
  this class of equations. This is joint work with Mat Langford\, Universit
 y of Tennessee Knoxville.\n\n \n\nFor zoom meeting ID and password please 
 contact dmitry.jakobson [at] mcgill.ca\n
DTSTART:20200429T173000Z
DTEND:20200429T183000Z
SUMMARY:Julian Scheuer (Freiburg)
URL:/mathstat/channels/event/julian-scheuer-freiburg-3
 21864
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