On large solutions for fractional Hamilton-Jacobi equations.

Abstract: In this talk I will report some multiplicity results for large solutions of fractional Hamilton-Jacobi equations posed on a bounded domain, subject to exterior Dirichlet conditions. We construct large solutions using the method of sub and supersolutions, following the classical approach of J.M. Lasry and P.L. Lions for second-order equations with subquadratic gradient growth. We identify two classes of solutions: the one coming from the natural scaling of the problem; and a one-parameter family of solutions, different from the previous, which can be formally described as a lower-order perturbation of blow-up fractional harmonic functions. Joint work with Alexander Quaas and Gonzalo Dávila (UTFSM-Chile).