Fundamental solutions and intertwining kernels in Heisenberg-type groups

Abstract

In this talk we discuss the conformal fractional powers of the horizontal Laplacian in Heisenberg-type groups. We present a new approach, based on the heat kernels of suitable extension operators, to the derivation of the fundamental solutions for these nonlocal operators and to the explicit construction of the Aubin-Talenti type functions. Frequent comparisons with the Euclidean case of the powers of the Laplacian will be made, focusing both on the similarities of the intertwining properties and on the main differences between the underlying heat kernels. The talk is based on a joint project with N. Garofalo.

Eventi passati

È possibile consultare gli eventi del precedente ciclo alla pagina dedicata