Abstract:
This talk will be a brief survey of recent results on the regularity of maximal operators acting on Sobolev and BV functions. Most of such problems can be posed either in a continuous or in a discrete setting. We will present some results for the classical Hardy-Littlewood maximal operator, for operators of convolution type (associated to elliptic and parabolic PDE’s) and also for fractional maximal operators.
The talk will be accessible to a broad audience.