2008/02/14 by Ching-Lung Lin, Gen Nakamura, Lin, Ching-Lung +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.0802.1983
openalex publication_date 2008/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen phases. A key strategy in the proof is to derive doubling inequalities via three-sphere inequalities. Our method can also be applied to certain elliptic systems with similar singular coefficients.