Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 256, Issue 9, Pages 2842-2866Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2008.10.017
Keywords
Linearization; Stability; Inverse backscattering
Categories
Funding
- NSF [DMS-0800428]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0800428] Funding Source: National Science Foundation
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We propose an abstract approach to prove local uniqueness and conditional Holder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization A, we need a stability estimate for A as well. That condition is satisfied in particular, if A*A is an elliptic pseudo-differential operator. We apply this scheme to show uniqueness and Holder stability for the inverse backscattering problem for the acoustic equation near a constant sound speed. (C) 2008 Elsevier Inc. All rights reserved.
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