  In a two-dimensional microwave chaotic cavity ohmic losses located at the
contour of the cavity result in different broadenings of different modes. We
provide an analytic description and establish the link between such an
inhomogeneous damping and the complex (non-real) character of biorthogonal wave
functions. This substantiates the corresponding recent experimental findings of
Barthelemy et al. [Europhys. Lett. 70, 162 (2005)].
