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

Harsh Prasad

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arXiv · 2604.06981

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

Harsh Prasad

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Abstract

We show that the global unique continuation principle holds for the parabolic fractional $p-$Laplace equation with very rough potentials $V(x,t) \in L^{p'}_tW^{-s,p'}_x$. 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.

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Harsh Prasad. 2026-04-08. Global UCP For Parabolic Fractional $p$-Laplace Equation With Very Rough Potentials. https://arxiv.org/abs/2604.06981

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