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X-WR-CALDESC:FAU DCN-AvH. Chair for Dynamics, Control, Machine Learning and Numerics -Alexander von Humboldt Professorship
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DTSTART;TZID=Europe/Berlin:20230315T110000
DTEND;TZID=Europe/Berlin:20230315T120000
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SUMMARY:Parabolic trajectories and the Harnack inequality
DESCRIPTION:Next Wednesday March 15, 2023:\nOrganized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)\nTitle: Parabolic trajectories and the Harnack inequality \nSpeaker: Lukas Niebel\nAffiliation: Ulm University\nAbstract. In this talk, we will study the Harnack inequality for weak solutions to a parabolic diffusion problem with rough coefficients. This is often referred to as De Giorgi-Nash-Moser theory.\nIn the first part, I will present the proof of the Harnack inequality due to Moser (1971). He combines a weak L1-estimate for the logarithm of supersolutions with Lp −L∞-estimates and a lemma due to Bombieri and Giusti. His method has been applied to nonlocal parabolic problems (Kassmann and Felsinger 2013), time-fractional diffusion equations (Zacher 2013), discrete problems (Delmotte 1999) and many more. In each of these works, the proof of the weak L1-estimate follows more or less the strategy of Moser and is based on a Poincaré inequality.\nIn the second part, I will present a novel proof of this weak L1-estimate, based on parabolic trajectories, which does not rely on any Poincaré inequality. The approach is entirely different from Moser’s proof and gives a very nice geometric interpretation of the result. The argument does not treat the temporal and spatial variables separately but considers both variables simultaneously. \nIn the end, I will draw some connections to Li-Yau inequalities and kinetic equations. \nThis is based on joint work with Rico Zacher (Ulm University).\nWHERE?\nOn-site / Online\nOn-site:\nRoom Übung 4\n1st. floor. Department Mathematik. Friedrich-Alexander-Universität Erlangen-Nürnberg\nCauerstraße 11, 91058 Erlangen\nGPS-Koord. Raum: 49.573572N, 11.030394E\nOnline:\nZoom meeting link\nMeeting ID: 614 4658 159 | PIN code: 914397\nThis event on LinkedIn\n
URL:https://dcn.nat.fau.eu/events/parabolic-trajectories-and-the-harnack-inequality/
ORGANIZER;CN=FAU DCN-AvH:MAILTO:
CATEGORIES:FAU DCN-AvH Jr. Seminar,Seminar/Talk
LOCATION:DDS, Friedrich-Alexander-Universität Erlangen-Nürnberg
ATTACH;FMTTYPE=image/png:https://dcn.nat.fau.eu/wp-content/uploads/FAUDCNAvH-JrSeminar-lNiebel-15mar2023.png
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