Raffaella Giova/Antonia Passarelli di Napoli: Widely degenerate parabolic problems

Speaker
Raffaella Giova, Parthenope University, Naples; Antonia Passarelli di Napoli, University Federico II, Naples

Abstract
We present some regularity results for the gradient of the weak solutions to strongly degenerate parabolic PDE’s that arise gas filtration problems. More precisely, we will present a continuity result of a suitable function of the gradient as well as a second order regularity result of a nonlinear function of the spatial gradient Du, which in turn implies the existence of the weak time derivative. The results are obtained in collaboration with V. Bögelein (University of Salzburg), F. Duzaar (University of Salzburg) and R. Giova (University of Naples “Parthenope”) and with P. Ambrosio (University of Naples “Federico II”) and A. Gentile (Università Politecnica delle Marche).