An elliptic equation with fractional nonlinearity

We will present results concerning existence and uniqueness of solutions to a nonlinear equation driven by an operator arising from the superposition of a Laplacian and a signed power of a fractional Laplacian. Of particular interest are the boundary conditions naturally associated to the equation. We will also go over a couple of strongly related problems. This is a joint work with M. Cozzi (UniMi).