Harnack Inequality and Self-Similar Solutions for Fully Nonlinear Fractional Parabolic Equations

We find bounds for the principal eigenvalue and eigenfunction associated to the existence of self-similar solutions to a fully nonlinear parabolic problem. In contrast with the local case, the upper and lower bounds for the eigenfunction are of the same polynomial order | x| -(N+2s). In order to accomplish this we prove a Harnack inequality for general nonlocal elliptic equations with zero order terms. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.