Journal article
The Calderón problem for variable coefficients nonlocal elliptic operators
Communications in partial differential equations, v 42(12), pp 1923-1961
02 Dec 2017
Featured in Collection : UN Sustainable Development Goals @ Drexel
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.
Metrics
Details
- Title
- The Calderón problem for variable coefficients nonlocal elliptic operators
- Creators
- Tuhin Ghosh - University of Hong KongYi-Hsuan Lin - University of WashingtonJingni Xiao - Hong Kong Baptist University
- Publication Details
- Communications in partial differential equations, v 42(12), pp 1923-1961
- Publisher
- Taylor & Francis
- Grant note
- Y.-H. Lin is partially supported by MOST of Taiwan under the project 160-2917-I-564-048 and J. Xiao was partly supported by the Mr. Kwok Yat Wai and Madam Kwok Chung Bo Fun Graduate School Development Fund.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000418083700003
- Scopus ID
- 2-s2.0-85034097402
- Other Identifier
- 991021878114904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied