Determining coefficients for a fractional p-Laplace equation from exterior measurements

2022/12/06 by Manas Kar, Yi‐Hsuan Lin, Kar, Manas +3
Computer Science · Engineering · Mathematics · #42B37 #46F12 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Primary 35R30 #Stability and Controllability of Differential Equations #secondary 26A33

paper · pdf · doi:10.48550/arxiv.2212.03057

openalex publication_date 2022/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an inverse problem of determining the coefficients of a fractional p -Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction formula in the region where the exterior measurements are performed. This formula is then used to establish a global uniqueness result for real-analytic coefficents. In addition, we also derive a stability estimate for the unique determination of the coefficients in the exterior measurement set.

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