Department of Mathematics

Geometry and Topology

  •  Jeffrey Case, Penn State
  •  A geometric approach to fractional powers of the Laplacian and sharp Sobolev trace inequalities
  •  09/22/2020
  •  3:00 PM - 4:00 PM
  •  Online (virtual meeting)

A seminal paper of Caffarelli and Silvestre identifies fractional powers of the Laplacian on Euclidean space as Dirichlet-to-Neumann operators. In this talk, I will use conformal geometry to generalize their approach to Riemannian manifolds. More specifically, I will present multiple (equivalent) definitions of (conformally covariant) operators with principal symbol that of a fractional power of the Laplacian. I will also discuss how these operators lead to a simple derivation of a broad family of sharp Sobolev trace inequalities. https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09

 

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