597	RWTH Publication No: 956766        2018
TITLE	Identifiability of Diffusion Coefficients for Source Terms of Non-Uniform Sign
AUTHORS	Markus Bachmayr, Van Kien Nguyen
ABSTRACT	The problem of recovering a diffusion coefficient a in a second-order elliptic partial differential equation from a corresponding solution u for a given right-hand 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: 1007-1021