BEGIN:VCALENDAR VERSION:2.0 METHOD:PUBLISH PRODID:-//Missouri State University/Calendar of Events//EN CALSCALE:GREGORIAN X-WR-TIMEZONE:America/Chicago BEGIN:VTIMEZONE TZID:America/Chicago BEGIN:DAYLIGHT TZOFFSETFROM:-0600 TZOFFSETTO:-0500 DTSTART:20070311T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU TZNAME:CDT END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0500 TZOFFSETTO:-0600 DTSTART:20071104T020000 RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU TZNAME:CST END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:7d7cebda-b755-4fbd-8be2-c6ce30bc84a7.173187@calendar.missouristate.edu CREATED:20161025T165517Z LAST-MODIFIED:20161025T165517Z LOCATION:Cheek Hall 301 SUMMARY:Mathematics Colloquium: Minimizers for Nonconvex Variational Probl ems in the Plane via Convex/Concave Rearrangements DESCRIPTION:Recently\, A. Greco utilized convex rearrangements to present some new and interesting existence results for noncoercive functionals in the calculus of variations. Moreover\, the integrands were not necessari ly convex. In particular\, using convex rearrangements permitted him to e stablish the existence of convex minimizers essentially considering the u niform convergence of the minimizing sequence of trajectories and the poi ntwise convergence of their derivatives. The desired lower semicontinuity property is now a consequence of Fatou's lemma.\n\n\nIn this paper we po int out that such an approach was considered in the late 1930s in a serie s of papers by E. J. McShane for problems satisfying the usual coercivity condition.  Our goal is to survey some of McShane's results and compare them with Greco's work.  In addition\, we will update some hypotheses tha t McShane made by making use of a result due to T. S. Angell on the avoid ance of the Lavrentiev phenomenon.  X-ALT-DESC;FMTTYPE=text/html:<html><head><title></title></head><body><p>Re cently\, A. Greco utilized convex rearrangements to present some new and interesting existence results for noncoercive functionals in the calculus of variations. Moreover\, the integrands were not necessarily convex. In particular\, using convex rearrangements permitted him to establish the existence of convex minimizers essentially considering the uniform conver gence of the minimizing sequence of trajectories and the pointwise conver gence of their derivatives. The desired lower semicontinuity property is now a consequence of Fatou's lemma.</p>\n<p>In this paper we point out th at such an approach was considered in the late 1930s in a series of paper s by E. J. McShane for problems satisfying the usual coercivity condition .&nbsp\; Our goal is to survey some of McShane's results and compare them with Greco's work.&nbsp\; In addition\, we will update some hypotheses t hat McShane made by making use of a result due to T. S. Angell on the avo idance of the Lavrentiev phenomenon.&nbsp\;</p></body></html> DTSTART;TZID=America/Chicago:20161102T153000 DTEND;TZID=America/Chicago:20161102T163000 SEQUENCE:0 URL:http://Math@missouristate.edu CATEGORIES:Public,Current Students,Faculty,Staff END:VEVENT END:VCALENDAR