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Author

Harsh Prasad

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Preprint Aug 2026

Strong Unique Continuation for Fractional Schr\"odinger Operators

We prove the strong unique continuation property for the fractional Schr\"odinger equation \[ (-\Delta)^s u=Vu \] with scaling-critical potentials $ V\in L^{\frac{n}{2s}}_{\mathrm{loc}}$ for all $0<s<1$. Our result constitutes the nonlocal counterpart to the classical Jerison--Kenig result for Schr\"odinger operators.

Harsh Prasad · 0 citations
Preprint Sep 2026

Harnack Inequality for Parabolic Fractional $p$-Laplace Equations

We establish an intrinsic Harnack inequality with an optimal tail term for weak solutions of parabolic fractional $p$-Laplace equations with $p>2$ and $s\in(0,1)$ whose kernels are symmetric, measurable, and comparable to $|x-y|^{-n-sp}$. It constitutes the nonlocal analogue of the intrinsic Harnack inequality of DiBen...

Harsh Prasad · 0 citations

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