Marcelina Mocanu
Vasile Alecsandri University of Bacău, Bacău, Romania

In this talk we summarize several results on the regularity of Orlicz-Sobolev functions on a metric space with a doubling measure and present some of their generalizations to the case where the role of the Orlicz space is played by a more general rearrangement invariant Banach function space.

The topics to be discussed include the density of Lipschitz functions in Sobolev-type spaces, aspects of pointwise behavior of Orlicz-Sobolev functions (quasicontinuity, Lebesgue points) and various types of differentiability (approximate, almost everywhere, in $L^{\Phi }$- sense). Poincaré inequalities and maximal operators of Hardy-Littlewood type are key tools. Some regularity properties have been recently generalized to the setting of Musielak-Orlicz-Sobolev spaces, a flexible framework for the study of nonlinear PDE's and variational problems.