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.
On the Unique Continuation Principle for a Class of Translation Invariant Nonlocal Operators
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abstract
The unique continuation property (UCP) for an operator $A$ says that, if $Au = 0 = u$ holds on an open set $G$, then one has $u=0$ everywhere. We establish necessary and sufficient conditions for the UCP for the class of L\'evy operators. We prove a connection between the UCP of the L\'evy operator and its resolvent. Our results are applied to obtain a new elementary proof of the UCP for the fractional Laplace operator, and for certain functions (Bernstein functions) of the discrete Laplace operator.
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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.