Monday, June 24, 2019 - 3:45pm - 4:45pm
Nicole Vorderobermeier (Universität Salzburg)
How nice are critical knots of knot energies? We already know that critical knots of the Möbius energy are smooth. This leads to the question whether critical knots of the Möbius energy are not only smooth, but also analytic. In this lecture, we give a short overview on the regularity results for the Möbius energy and present techniques with which the open question on the analyticity was solved. To the best of our knowledge, this is the first analyticity result in the context of non-local differential equations.
Saturday, June 25, 2016 - 11:30am - 12:20pm
John Mallet-Paret (Brown University)
While delay differential equations with variable delays may have a superficial appearance of analyticity, it is far from clear in general that a global bounded solution $x(t)$ (namely, a bounded solution defined for all time $t$, such as a solution lying on an attractor) is an analytic function of $t$. Indeed, very often such solutions are not analytic, although they are often $C^\infty$. In this talk we provide sufficient conditions both for analyticity and for non-analyticity (but $C^\infty$ smoothness) of such solutions.
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