  We study, within the Ginzburg-Landau (GL) theory of phase transitions, how
elastic deformations in a supersolid lead to local changes in the supersolid
transition temperature. The GL theory is mapped onto a Schrodinger-type
equation with an effective potential that depends on local dilatory strain. The
effective potential is attractive for local contractions and repulsive for
local expansion. Different types of elastic deformations are studied. We find
that a contraction (expansion) of the medium that may be brought about by,
e.g., applied stress leads to a higher (lower) transition temperature as
compared to the unstrained medium. In addition, we investigate edge
dislocations and illustrate that the local transition temperature may be
increased in the immediate vicinity of the dislocation core. Our analysis is
not limited to supersolidity. Similar strain effects should also play a role in
superconductors.
