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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
The Calder\'on problem for variable coefficients nonlocal elliptic operators
02 Aug 2017
Abstract
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 GhoshYi-Hsuan LinJingni Xiao
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021878114504721