Special Session 35: Elliptic PDEs: singularities, discontinuities, and nonlinear phenomena

The obstacle problem for the $p$-Laplacian
Annamaria Barbagallo
University of Naples Federico II
Italy
Co-Author(s):    Umberto Guarnotta
Abstract:
The purpose of the talk is to prove the existence of a solution to the obstacle problem involving the $p$-Laplacian operator, in a setting where the reaction term is singular at zero and exhibits strong discontinuities. Notably, no restriction is placed on the discontinuity set having zero Lebesgue measure. Lastly, it is shown that the solution lies in the space $C^{1, \alpha}$ outside the contact set.