Date | 2022-07-04 |
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Speaker | Armin Schikkora |

Dept. | University of Pittsburgh, USA |

Room | 27-220 |

Time | 15:00-17:00 |

Abstract:

I will report about the theory of minimizing and critical knots under a set of scale invariant knot energies, the so-called tangent-point energy.

We obtain lower semicontinuity and weak Sobolev-convergence of minimizing sequences to critical points away from finitely many points in the domain. Extending earlier work on Moebius-, and O'Hara energies we also obtain regularity for such critical points.

This is based on joint work with S. Blatt, Ph. Reiter, and N. Vorderobermeier.

Abstract: I will report on progress obtained for the W^{s,p}-regularity theory for nonlocal/fractional equations of differential order 2s with bounded measurable Kernel.

Namely, under (not yet optimal) assumptions on the kernel we obtain W^{t,p}-estimates for suitable right-hand sides, where s< t < 2s.

Technically we compare such equations via a commutator estimate to a simpler fractional equation.

Based on joint works with M. Fall, T. Mengesha, S. Yeepo.

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