On unique continuation in measure for fractional heat equations

Abstract

We prove a theorem of unique continuation in measure for nonlocal equations of the type $({\partial }_t-\Delta {)}^{s}u=V(x,t)u$, for $0<s<1$. Our main result, Theorem 1.1, establishes a delicate nonlocal counterpart of the unique continuation in measure for the local case $s=1$.