Programa de Pós-Graduação em Matemática

The uncharted territory of Wα,1 Sobolev spaces

Prof. Augusto Ponce

Date: 18th February 10:00 am - 10:45 am (UTC -3) Link: PPGM/UFSCar Youtube channel

Abstract: I will address properties of the fractional Sobolev space Wα,1(RN) which cannot be answered by classical representation formulas from Harmonic Analysis, for any exponent α > 0. They can be handled instead in terms of a strong capacitary inequality which is based itself on a new geometric boxing inequality that connects the Hausdorff content of dimension N − α and the fractional perimeter of order 0<α<1. These results have been obtained in collaboration with D. Spector (Okinawa, Japan).