The Calderón problem for variable coefficients nonlocal elliptic operators

By Tuhin Ghosh, Yi-Hsuan Lin, Jingni Xiao. 2017

117 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78d912891f91ab94bb17b5158b8f1b8aca1dd984

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The higher order fractional Calderón problem for linear local operators: Uniqueness (2020, background): “Other variants of the fractional Calderón problem include semilinear fractional (magnetic) Schrödinger equation [19, 20, 24, 25], fractional heat equation [21, 35] and fractional conductivity equation [8] (see also [6, 13] for equations arising from a nonlocal Schrödinger-type elliptic operator).”
Monotonicity-based inversion of the fractional Schr\"odinger equation (2017, methodology): “, [32, 30].”