Evento

Seminari di Analisi

Seminari di Analisi
  • Seminari di Analisi
  • 2025-06-27T11:00:00+02:00
  • 2025-06-27T12:00:00+02:00
  • Seminario in presenza del Prof. Mirco Piccinini (Università di Pisa) dal titolo: "Nonlocal theory for fractional kinetic equations" A seguire, il seminario della Prof.ssa Francesca Anceschi (Università Politecnica delle Marche) dal titolo "Geometrical methods for regularity theory for kinetic equations"
Seminario in presenza del Prof. Mirco Piccinini (Università di Pisa) dal titolo: "Nonlocal theory for fractional kinetic equations" A seguire, il seminario della Prof.ssa Francesca Anceschi (Università Politecnica delle Marche) dal titolo "Geometrical methods for regularity theory for kinetic equations"

Venerdì 27 Giugno, dalle ore 11:00
Aula C2, Palazzo Manfredini

Abstract 1)
We extend the De Giorgi-Nash-Moser theory to a class of nonlocal hypoelliptic equations naturally arising in kinetic theory, which combine a first-order skew-symmetric operator with an elliptic operator involving fractional derivatives along only part of the coordinates. Under sufficient integrability along the transport variables on the nonlocal tail, we prove the first local $L^\infty$ estimate for this class of equations. Then, we establish the first full Harnack inequality for solutions to kinetic integral equations under the aforementioned tail summability assumption, which appears in clear accordance with the very recent counterexample by Kassmann and Weidner (Adv. in Math., 2024). This is based on series of papaers by F. Anceschi, M. Kassmann, A. Loher, G. Palatucci, M. Weidner and myself.


Abstract 2)
We plan to analyse from a geometrical perspective some quantitative regularity results for kinetic equations.
This talk is based on two recent works in collaboration with various authors (Dietert, Guerand, Loher, Mouhot, Rebucci and Palatucci, Piccinini).

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