A bridge between Sobolev and Escobar inequalities and beyond
Martedì 28 febbraio 2017 ore 14.30, Edificio Matematica, aula M1.6 (I piano)
Relatore: Robin Neumayer (University of Texas at Austin, US)
Abstract: In this talk, we show that the classical Sobolev and Escobar inequalities are embedded into the same one-parameter family of sharp trace-Sobolev inequalities on half-spaces. We prove each inequality in this one-parameter family and characterize equality cases using a variation of a well-known mass transportation argument. The case of the Dirichlet energy corresponds to a family of variational problems on conformally flat metrics, whose absolute minimizers interpolate between conformally flat spherical and hyperbolic geometries, passing through the Euclidean geometry defined by the fundamental solution of the Laplacian.
This is joint work with Francesco Maggi.
Ospiti: G.P. Leonardi.
[Ultimo aggiornamento: 23/02/2017 15:37:38]