Yingying Cai

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math.AP2025

Quantitative unique continuation for Neumann problem in planar $C^{1, α}$ domains

Yingying Cai, Jiuyi Zhu, Jinping Zhuge

In this paper, we study the quantitative unique continuation property of the second-order elliptic operators under the vanishing Neumann boundary condition over $C^{1, α}$ or convex…

math.AP2024

Unique continuation at the boundary for divergence form elliptic equations on quasiconvex domains

Yingying Cai

Let $Ω \subset R^{d}$ be a quasiconvex Lipschitz domain and $A (x)$ be a $d \times d$ uniformly elliptic, symmetric matrix with Lipschitz coefficients. Assume a nontrivial $u$ …

math.AP2024

The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes

Yingying Cai, Jinping Zhuge

Let $P$ be a bounded $n$ -dimensional Lipschitz polytope, and let $φ_{λ}$ be a Dirichlet Laplace eigenfunction in $P$ corresponding to the eigenvalue $λ$ . We show that the $(n - 1)$ -dim…

Quantitative unique continuation for Neumann problem in planar C1,α domains

Unique continuation at the boundary for divergence form elliptic equations on quasiconvex domains

The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes

Quantitative unique continuation for Neumann problem in planar $C^{1, α}$ domains