  A detailed theoretical interpretation of the Josephson interference
experiment between Sr$_2$RuO$_4$ and Pb reported by Kidwingira \textit{et al}
is given. Assuming chiral p-wave pairing symmetry a Ginzburg-Landau theory is
derived in order to investigate the structure of domain walls between chiral
domains. It turns out that anisotropy effects of the Fermi surface and the
orientation of the domain walls are essential for their internal structure.
Introducing a simple model for a Josephson junction the effect of domain walls
intersecting the interface between Sr$_2$RuO$_4$ and Pb is discussed. It is
shown that characteristic deviations of the Fraunhofer interference pattern for
the critical Josephson current as a function of the magnetic field occurs in
qualitative agreement with the experimental finding. Moreover the model is able
also to account for peculiar hysteresis effects observed in the experiment.
