  The Lamb shift (self-energy) of an elliptic dielectric microcavity is
studied. We show that the size of the Lamb shift, which is a small energy shift
due to the system-environment coupling in the quantum regime, is dependent on
the geometry of the boundary conditions. It shows a global transition depending
on the eccentricity of the ellipsis. These transitions can be classified into
three types of decay channels known as whispering-gallery modes,
stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are
manifested through the Poincar\'{e} surface of section with the Husimi
distribution function in classical phase space. It is found that the similarity
(measured in Bhattacharyya distance) between the Husimi distributions below
critical lines of two different modes increases as the difference of their
self-energies decreases when the quality factors of the modes are on the same
order of magnitude.
