BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Julian Scheuer (Cardiff University) DTSTART:20200811T170000Z DTEND:20200811T180000Z DTSTAMP:20260423T035031Z UID:OSGA/23 DESCRIPTION:Title: Co ncavity of solutions to elliptic equations on the sphere\nby Julian Sc heuer (Cardiff University) as part of Online Seminar "Geometric Analysis"\ n\n\nAbstract\nAn important question in PDE is when a solution to an ellip tic\nequation is concave. This has been of interest with respect to the sp ectrum of\nlinear equations as well as in nonlinear problems. An old techn ique going back\nto works of Korevaar\, Kennington and Kawohl is to study a certain two-point\nfunction on a Euclidean domain to prove a so-called c oncavity maximum principle\nwith the help of a first and second derivative test. To our knowledge\, so far\nthis technique has never been transferre d to other ambient spaces\, as the\nnonlinearity of a general ambient spac e introduces geometric terms into the\nclassical calculation\, which in ge neral do not carry a sign. In this talk we\nhave a look at this situation on the unit sphere. We prove a concavity maximum\nprinciple for a broad cl ass of degenerate elliptic equations via a careful\nanalysis of the spheri cal Jacobi fields and their derivatives. In turn we obtain\nconcavity of s olutions to this class of equations. This is joint work with Mat\nLangford \, University of Tennessee Knoxville.\n LOCATION:https://researchseminars.org/talk/OSGA/23/ END:VEVENT END:VCALENDAR