Submitted Paper

Inserted: 4 nov 2026

Year: 2026

Abstract:

With the aim of extending to parabolic equations the framework developed by the first three authors in Dipierro, Savin, and Valdinoci, Rev. Mat. Iberoam. (2019), we introduce a notion of (viscosity) solutions for the space-fractional heat equation modulo $k$. In turn, we are able to define $s$-caloric functions with polynomial growth at infinity, showing also related Schauder estimates, a Liouville-type result, and a stability property with respect to the $L^\infty_{\rm{loc}}$-convergence.