  An inverse problem to identify unknown coefficients of a partial differential
equation by a single interior measurement is considered. The equation
considered in this paper is a strongly elliptic second order scalar equation
which can have complex coefficients in a bounded domain with $C^2$ boundary and
single interior measurement means that we know a given solution of the equation
in this domain. The equation includes some model equations arising from
acoustics, viscoelasticity and hydrology. We assume that the coefficients are
piecewise analytic. Our major result is the local H\"older stability estimate
for identifying the unknown coefficients. If the unknown coefficients is a
complex coefficient in the principal part of the equation, we assumed a
condition which we named admissibility assumption for the real part and
imaginary part of the difference of the two complex coefficients. This
admissibility assumption is automatically satisfied if the complex coefficients
are real valued. For identifying either the real coefficient in the principal
part or the coefficient of the 0-th order of the equation, the major result
implies the global uniqueness for the identification.
