BEGIN:VCALENDAR VERSION:2.0 PRODID:-//132.216.98.100//NONSGML kigkonsult.se iCalcreator 2.20.4// BEGIN:VEVENT UID:20250810T024417EDT-9521Pzz8Pu@132.216.98.100 DTSTAMP:20250810T064417Z DESCRIPTION:Title: Borderline Variational problems for fractional Hardy-Sch rödinger operators\n Abstract: In this talk\, we investigate the existence of ground state solutions associated to the fractional Hardy-Schrödinger o perator on Euclidean space and its bounded domains. In the process\, we ex tend several results known about the classical Laplacian to the non-local operators described by its fractional powers. Our analysis show that the m ost important parameter in the problems we consider is the intensity of th e corresponding Hardy potential. The maximal threshold for such an intensi ty is the best constant in the fractional Hardy inequality\, which is comp utable in terms of the dimension and the fractional exponent of the Laplac ian. However\, the analysis of corresponding non-linear equations in borde rline Sobolev-critical regimes give rise to another threshold for the allo wable intensity. Solutions exist for all positive linear perturbations of the equation\, if the intensity is below this new threshold. However\, onc e the intensity is beyond it\, we had to introduce a notion of Hardy-Schrö dinger Mass associated to the domain under study and the linear perturbati on. We then show that ground state solutions exist when such a mass is pos itive. We then study the effect of non-linear perturbations\, where we sho w that the existence of ground state solutions for large intensities\, is determined by a subtle combination of the mass (i.e.\, the geometry of the domain) and the size of the nonlinearity of the perturbations. \n DTSTART:20171011T173000Z DTEND:20171011T183000Z LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue Sherbrooke Ouest SUMMARY:Shaya Shakerian (University of British Columbia) URL:/mathstat/channels/event/shaya-shakerian-universit y-british-columbia-275531 END:VEVENT END:VCALENDAR