The Calderón problem for variable coefficients nonlocal elliptic operators. Issue 12 (2nd December 2017)

• Record Type: Journal Article
• Authors: Ghosh, Tuhin; Lin, Yi-Hsuan; Xiao, Jingni
• Is Part Of: Communications in partial differential equations. Volume 42:Issue 12(2017)
• Page Start: 1923
• Page End: 1961
• Publication Date: 2017-12-02
• Subjects: Almgren's frequency function -- anisotropic -- Ap weight -- degenerate elliptic equations -- doubling inequality -- nonlocal Schrödinger equation -- Runge approximation property -- The Calderón problem -- unique continuation principle; 35R30 -- 26A33 -- 35J10 -- 35J70; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2017.1390681
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: In this paper, we introduce an inverse problem of a Schrödinger type variable nonlocal elliptic operator (−∇⋅( A ( x )∇)) s + q ), for 0< s <1. We determine the unknown bounded potential q from the exterior partial measurements associated with the nonlocal Dirichlet-to-Neumann map for any dimension n ≥2. Our results generalize the recent initiative [18 ] of introducing and solving inverse problem for fractional Schrödinger operator ((− Δ ) s + q ) for 0< s <1. We also prove some regularity results of the direct problem corresponding to the variable coefficients fractional differential operator and the associated degenerate elliptic operator.