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In this work we start from the assumption that normal solid to supersolid(NS-SS) phase transition is continuous, and develop a phenomenological Landautheory of the transition in which superfluidity is coupled to the elasticity ofthe crystalline $^4$He lattice. We find that the elasticity does not affect theuniversal properties of the superfluid transition, so that in an unstressedcrystal the well-known $\lambda$-anomaly in the heat capacity of the superfluidtransition should also appear at the NS-SS transition. We also find that theonset of supersolidity leads to anomalies in the elastic constants near thetransition; conversely, inhomogeneous strains in the lattice can induce localvariations of the superfluid transition temperature, leading to a broadenedtransition.Comment: 4 page

Squeezing Superfluid from a Stone: Coupling Superfluidity and Elasticity in a Supersolid