A simple proof establishes the strong-type unique continuation principle for the fractional p-Laplacian (−Δ_p)^s for a range of s and p, extending to strong solutions of the fractional nonlinear Schrödinger equation.
Global UCP For Parabolic Fractional $p$-Laplace Equation With Very Rough Potentials
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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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math.AP 1years
2026 1verdicts
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A strong-type unique continuation principle for the fractional $p$-Laplacian
A simple proof establishes the strong-type unique continuation principle for the fractional p-Laplacian (−Δ_p)^s for a range of s and p, extending to strong solutions of the fractional nonlinear Schrödinger equation.