Large or boundary blow-up solutions — namely, solutions to elliptic Dirichlet problems prescribed to attain the value $+\infty$ at the boundary — are a useful tool in the analysis of nonlinear PDEs, whereas they show a deep connection with geometrical and probabilistic problems.

A systematic study of these solutions originates by the independent works of Keller (1957) and Osserman (1957), but the topic is even more classical and dates back to Bieberbach (1930).

We want to study whether and under what assumptions this boundary explosion can be spotted also in a fractional nonlocal framework, in which the fractional Laplacian operator is known to lose smoothness at the boundary. We will also give some characterization of the asymptotic behaviour and we will compare it with the one coming from the classical theory.