  We investigate the effects of strain on superconductivity with particular
reference to SrTiO$_3$. Assuming that a ferroelectric mode that softens under
tensile strain is responsible for the coupling, an increase in the critical
temperature and range of carrier densities for superconductivity is predicted,
while the peak of the superconducting dome shifts towards lower carrier
densities. Using a Ginzburg-Landau approach in 2D, we find a linear dependence
of the critical temperature on strain: if the couplings between the order
parameter and strains in different directions differ while their sum is fixed,
different behaviours under uniaxial and biaxial (uniform) strain can be
understood.
