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SUMMARY:Giona Veronelli (Università di Milano-Bicocca)
DTSTART:20210210T170000Z
DTEND:20210210T180000Z
DTSTAMP:20260423T021306Z
UID:HAeS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HAeS/10/">So
 bolev spaces on manifolds with lower bounded curvature</a>\nby Giona Veron
 elli (Università di Milano-Bicocca) as part of Harmonic analysis e-semina
 rs\n\n\nAbstract\nThere are several notions of Sobolev spaces on a Riemann
 ian manifold: from the operator theory viewpoint it is natural to consider
  Sobolev functions defined by taking the $L^p$ norms of functions and of p
 owers of their Laplacian. Instead\, the regularity theory of elliptic equa
 tions involves Sobolev functions defined  via the $L^p$ norm of all the de
 rivatives up to a certain order. Moreover\, Sobolev spaces can be characte
 rized via compactly supported smooth approximations.\nIn this talk\, we wi
 ll focus on non-compact manifolds with lower bounded curvature. We will di
 scuss some results giving the (non)-equivalence between the different Sobo
 lev spaces. In particular\, we will highlight the role played in the theor
 y by the Calderon-Zygmund inequality and the Bochner formulas\, and we wil
 l sketch how to exploit singular metric spaces (e.g. Alexandrov or RCD) as
  a tool to construct smooth counterexamples.\n
LOCATION:https://researchseminars.org/talk/HAeS/10/
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