BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vitaly Moroz (Swansea University) DTSTART:20210416T121500Z DTEND:20210416T131500Z DTSTAMP:20260423T010636Z UID:EXACT/2 DESCRIPTION:Title: Th omas-Fermi type models for graphene.\nby Vitaly Moroz (Swansea Univers ity) as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theory\n\n\nAbstr act\nWe discuss density functional theories of Thomas-Fermi and Thomas-Fer mi-von Weizsacker type which describe the response of a single layer of gr aphene to an external electric charge. Mathematically\, this amounts to th e analysis of two nonlocal variational problems which involve Coulombic te rms and a Hardy type potential. We develop the variational framework in wh ich the proposed energy functionals admit minimizers and prove the uniquen ess and regularity of the ground states for the associated Euler-Lagrange equations which involve the fractional Laplacian. In addition\, we discuss positivity and decay rate of the ground states and present several open p roblems. This is a joint work with Jianfeng Lu (Duke) and Cyrill Muratov ( NJIT\, USA).\n\nPlease check for the zoom link 1 hour before the talk.\n LOCATION:https://researchseminars.org/talk/EXACT/2/ END:VEVENT END:VCALENDAR