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SUMMARY:Jimmy Scott (University of Pittsburgh)
DTSTART:20210330T170000Z
DTEND:20210330T180000Z
DTSTAMP:20260423T035034Z
UID:OSGA/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/54/">Fr
 actional Korn-Type Inequalities and Applications</a>\nby Jimmy Scott (Univ
 ersity of Pittsburgh) as part of Online Seminar "Geometric Analysis"\n\n\n
 Abstract\nWe show that a class of spaces of vector fields whose semi-norms
  involve the magnitude of ``directional" difference quotients is in fact e
 quivalent to the class of fractional Sobolev-Slobodeckij spaces. The equiv
 alence can be considered a Korn-type characterization of said Sobolev spac
 es. For vector fields defined on various classes of domains\, we obtain a 
 relevant form of the inequality. As an application\, we consider variation
 al problems associated to strongly coupled systems of nonlocal equations m
 otivated by a continuum mechanics model known as peridynamics. We use the 
 fractional Korn-type inequalities to characterize vector fields in associa
 ted energy spaces and obtain existence and uniqueness of solutions in frac
 tional Sobolev spaces.\n
LOCATION:https://researchseminars.org/talk/OSGA/54/
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