In this paper, we introduce an inverse problem of a Schr\"odinger type
variable nonlocal elliptic operator $(-\nabla\cdot(A(x)\nabla))^{s}+q)$, 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 $n\geq2$. Our results generalize the recent initiative [16] of
introducing and solving inverse problem for fractional Schr\"odinger operator
$((-\Delta)^{s}+q)$ 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.
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Details
Title
The Calder\'on problem for variable coefficients nonlocal elliptic operators
Creators
Tuhin Ghosh
Yi-Hsuan Lin
Jingni Xiao
Resource Type
Preprint
Language
English
Academic Unit
Mathematics
Other Identifier
991021878114504721
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