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BEGIN:VEVENT
UID:1348bb814dc778964a73c9f3754f590e
CATEGORIES:Learning Seminar on PDE and Applications
CREATED:20210208T125232
SUMMARY:Marcinkiewicz–Gagliardo weak-type formulas for Sobolev norms
LOCATION:zoom
DESCRIPTION: Abstract:  \n First-order Sobolev spaces have their norm defined in terms 
 of weak derivative whereas fractional Sobolev spaces are endowed with the G
 agliardo semi-norm controlling some integral of a differential quotient; th
 is results in a qualitative jump at the endpoint. These two perspectives we
 re reconciled through the introduction of a suitable corrective factor by J
 ean Bourgain, Haïm Brezis and Petru Mironescu have reconciled. In a recent 
 work in collaboration with Haïm Brezis (Rutgers, Technion Haifa and Sorbonn
 e) and Po-Lam Yung (Chinese University of Hong Kong and Australian National
  University), we are proving that Sobolev norms are equivalent to a Marcink
 iewicz weak-type quantity associated to the Gagliardo seminorm. I will pres
 ent how these estimates can be obtained through various tools of real analy
 sis.\n \n
X-ALT-DESC;FMTTYPE=text/html:<p><span style="font-family: Times New Roman; font-size: medium;"> <b><span
  style="color: black;"><span style="font-family: Times New Roman; font-size
 : medium;">Abstract:&nbsp;&nbsp;</span></span></b></span></p><p><span style
 ="font-family: Times New Roman; font-size: medium;"> <span style="color: bl
 ack; font-family: 'Calibri',sans-serif;"><span style="font-size: medium;">F
 irst-order Sobolev spaces have their norm defined in terms of weak derivati
 ve whereas fractional Sobolev spaces are endowed with the Gagliardo semi-no
 rm controlling some integral of a differential quotient; this results in a 
 qualitative jump at the endpoint. These two perspectives were reconciled th
 rough the introduction of a suitable corrective factor by Jean Bourgain, Ha
 ïm Brezis and Petru Mironescu have reconciled. In a recent work in collabor
 ation with Haïm Brezis (Rutgers, Technion Haifa and Sorbonne) and Po-Lam Yu
 ng (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 es
 timates can be obtained through various tools of real analysis.<span style=
 "color: black; font-family: 'Calibri',sans-serif; mso-fareast-font-family: 
 'Times New Roman';"><span style="font-size: medium;"></span></span></span><
 /span></span></p><p><span style="font-family: Times New Roman; font-size: m
 edium;"> </span></p>
CONTACT:Jean Van Schaftingen, UCLouvain, Belgium
X-EXTRAINFO:The talks will be held virtually:\nhttps://rutgers.zoom.us/j/92489375526?pw
 d=K0xyMEpHQXIrc0NLMEtqUWdSNHF4QT09#success\nMeeting ID:924 8937 5526Passcod
 e:565238\n
DTSTAMP:20260830T193453
DTSTART;TZID=America/New_York:20210209T124000
DTEND;TZID=America/New_York:20210209T144000
SEQUENCE:0
TRANSP:OPAQUE
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