Propagation of minima for nonlocal operators

Abstract

In this paper we state some sharp maximum principle, i.e. we characterize the geometry of the sets of minima for supersolutions of equations involving the $k$-\emph{th fractional truncated Laplacian} or the $k$-\emph{th fractional eigenvalue} which are fully nonlinear integral operators whose nonlocality is somehow $k$-dimensional.