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

Gradient regularity for quasilinear elliptic problems
Carlo Alberto Antonini
INdAM (National Institute of High Mathematics)
Italy
Co-Author(s):    
Abstract:
In this talk we will deal with quasilinear elliptic equations in divergence form $-\mathrm{div}\big(\mathcal{A}(x,Du)\big)=f$, modeled upon the $p$-Laplace and, more generally, the Orlicz-Laplace operator. We will discuss gradient regularity of solutions, both in the interior and up to the boundary, under Dirichlet or Neumann boundary conditions.