Global UCP For Parabolic Fractional $p$-Laplace Equation With Very Rough Potentials

Abstract

We show that the global unique continuation principle holds for the parabolic fractional $p-$Laplace equation with very rough potentials $V(x,t)\in L_t^{p^{\prime }}{W}_x^{-s,p^{\prime }}$. Whereas the result is new even for the fractional $p-$Laplace operator, the corresponding local problem remains open even with zero potential. The short proof eschews extension techniques and Carleman estimates.

7 pages; comments welcome!