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SUMMARY:Alessandro Pigati (Bocconi University)
DTSTART:20260520T090000Z
DTEND:20260520T110000Z
DTSTAMP:20260513T125028Z
UID:NCTS-GMT/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCTS-GMT/35/
 ">Anisotropic Allen-Cahn and convergence to anisotropic area</a>\nby Aless
 andro Pigati (Bocconi University) as part of NCTS international Geometric 
 Measure Theory seminar\n\n\nAbstract\nIn this talk we will introduce a PDE
  way to construct hypersurfaces\nwhich are critical for a generalization o
 f area\, based on an anisotropic\nintegrand. Namely\, we study energy conc
 entration for rescalings of an\nanisotropic version of Allen-Cahn.\n\nAfte
 r reviewing known existence and regularity results for minimizers\nand min
 -max solutions\, as well as the Allen-Cahn approximation in the\nisotropic
  case\, we will sketch a proof of the fact that energy of stable\ncritical
  points (of the rescaled Allen-Cahn functional) concentrates\nalong an int
 eger rectifiable varifold\, a weak notion of hypersurface\,\nusing stabili
 ty (or finite Morse index) to compensate for the lack of\nmonotonicity for
 mulas.\n\nAmong the technical ingredients\, we will see a generalization o
 f\nModica's bound and a diffuse version of the stability inequality for\nh
 ypersurfaces.\n\nThis is joint work with Antonio De Rosa (Bocconi Universi
 ty).\n
LOCATION:https://researchseminars.org/talk/NCTS-GMT/35/
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