Special Session 74: Recent advances in local and nonlocal PDEs

Singular p-Laplacian problems with discontinuous convection terms
Umberto Guarnotta
University of Catania
Italy
Co-Author(s):    Salvatore A. Marano
Abstract:
The talk is devoted to discuss existence of solutions to a p-Laplacian problem whose reaction is singular (i.e., it blows up when the solution approaches zero), convective (that is, it depends on the gradient of the solution), and possesses a null-measure set of discontinuity points. The techniques presented are based on regularization arguments, monotonicity techniques, regularity theory, locality properties, and measure-theoretical arguments.