Vectorial Nonlinear Potential Theory
Speaker: Tuomo Kuusi, Aalto University, Helsinki
Location: Warren Weaver Hall 1302
Date: Thursday, November 3, 2016, 11 a.m.
We discuss new pointwise potential estimates obtained for vectorial p-Laplacian involving measure data. The estimates allow to give sharp descriptions of fine properties of solutions which are the exact analog of the ones in classical linear potential theory. For instance, sharp characterizations of Lebesgue points and optimal regularity criteria for solutions are provided exclusively in terms of potentials. The validity of such estimates in the vectorial setting was an open problem for more than 20 years, and we recently settled this in collaboration with G. Mingione.