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RWTH Publication No: 956766 2018 
TITLE 
Identifiability of Diffusion Coefficients for Source Terms of NonUniform Sign 
AUTHORS 
Markus Bachmayr, Van Kien Nguyen 
ABSTRACT 
The problem of recovering a diffusion coefficient a in a secondorder elliptic partial differential equation from a corresponding solution u for a given righthand side f is considered, with particular focus on the case where f is allowed to take both positive and negative values. Identifiability of a from u is shown under mild smoothness requirements on a, f, and on the spatial domain D, assuming that either the gradient of u is nonzero almost everywhere, or that f as a distribution does not vanish on any open subset of D. Further results of this type under essentially minimal regularity conditions are obtained for the case of D being an interval, including detailed information on the continuity properties of the mapping from u to a. 
KEYWORDS 
Inverse problem, elliptic partial differential equation, identifiability, sets of finite perimeter, Hölder stability 
DOI 
10.3934/ipi.2019045 
PUBLICATION 
Inverse Problems and Imaging, 2019, Volume 13, Issue 5: 10071021 