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Learning Seminar on PDE and Applications

Marcinkiewicz–Gagliardo weak-type formulas for Sobolev norms

Jean Van Schaftingen, UCLouvain, Belgium

Location:  zoom
Date & time: Tuesday, 09 February 2021 at 12:40PM - 2:40PM

Abstract:  

First-order Sobolev spaces have their norm defined in terms of weak derivative whereas fractional Sobolev spaces are endowed with the Gagliardo semi-norm controlling some integral of a differential quotient; this results in a qualitative jump at the endpoint. These two perspectives were reconciled through the introduction of a suitable corrective factor by Jean Bourgain, Haïm Brezis and Petru Mironescu have reconciled. In a recent work in collaboration with Haïm Brezis (Rutgers, Technion Haifa and Sorbonne) and Po-Lam Yung (Chinese University of Hong Kong and Australian National University), we are proving that Sobolev norms are equivalent to a Marcinkiewicz weak-type quantity associated to the Gagliardo seminorm. I will present how these estimates can be obtained through various tools of real analysis.

The talks will be held virtually:
https://rutgers.zoom.us/j/92489375526?pwd=K0xyMEpHQXIrc0NLMEtqUWdSNHF4QT09#success
Meeting ID:924 8937 5526Passcode:565238

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