2023/07/29 by Long Tian, Xiaoping Yang, Tian, Long +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2307.15854
openalex publication_date 2023/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the quantitative unique continuation, propagation of smallness and measure bounds of nodal sets of solutions to the Buckling type equation \triangle2u+λ\triangle u-k2u=0 in a bounded analytic domain Ω⊆ℝn with the homogeneous boundary conditions u=0 and (∂ u)/(∂ν)=0 on ∂Ω, where λ, k are nonnegative real constants, and ν is the outer unit normal vector on ∂Ω. We obtain that, the upper bounds for the maximal vanishing order of u and the n-1 dimensional Hausdorff measure of the nodal set of u are both C(√λ+√(k)+1), where C is a positive constant only depending on n and Ω. Moreover, we also give a quantitative result of the propagation of smallness of u.