Yuan Zhang

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20202026

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4 papers · 1 filter

math.AP2026

On a Local Radial Rigidity Phenomenon of Elliptic Systems on Riemannian Manifolds

Yifei Pan, Yu Yan, Yuan Zhang

In this paper, we study local radial rigidity phenomena for a broad class of general-order elliptic systems on Riemannian manifolds via a reduction to singular ordinary differentia…

math.AP2024

Continuous Sobolev functions with singularity on arbitrary real-analytic sets

Yifei Pan, Yuan Zhang

Near every point of a real-analytic set in $R^{n}$ , we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W^{1, 1}_{lo…

math.AP2024

Unique continuation for a gradient inequality with $L^{n}$ potential

Adam Coffman, Yifei Pan, Yuan Zhang

We establish a unique continuation property for solutions of the differential inequality $∣\nabla u ∣ \leq V ∣ u ∣$ , where $V$ is locally $L^{n}$ integrable on a domain in $R^{n}$ .…

math.AP2024

On solutions to $- Δ u = V u$ near infinity

Yifei Pan, Yuan Zhang

We investigate the unique continuation property and the sign changing behavior of weak solutions to $- Δ u = V u$ near infinity under certain conditions on the blow-up rate of the pote…

On a Local Radial Rigidity Phenomenon of Elliptic Systems on Riemannian Manifolds

Continuous Sobolev functions with singularity on arbitrary real-analytic sets

Unique continuation for a gradient inequality with Ln potential

On solutions to −Δu=Vu near infinity

Unique continuation for a gradient inequality with $L^{n}$ potential

On solutions to $- Δ u = V u$ near infinity