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SUMMARY:Relaxation : are smooth functions still dense in Sobolev spaces un
 der energy constraints?
DTSTART:20260622T120000Z
DTEND:20260622T130000Z
DTSTAMP:20261013T125000Z
UID:indico-event-16317@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paulin Huguet (IMT - Université de Toulouse)\n\nIn 
 this presentation\, we introduce the notion of relaxation for integral fun
 ctionals in the one-dimensional case of the form $\\int_O^L f(x\,u(x)\,u'(
 x)) dx$\, as well as the concept of Lavrentiev gap between two function sp
 aces. We review two categories of results established in this field and pr
 esent a new result for Lagrangians satisfying regularity assumptions only 
 with respect to the state variable u(x). We then draw a sketch of its proo
 f using a geometric approach. If time permits\, we will conclude with a br
 ief discussion of relaxation in the space BV.\n\nhttps://indico.math.cnrs.
 fr/event/16317/
LOCATION:Salle Pellos (1R2-207)
URL:https://indico.math.cnrs.fr/event/16317/
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