Nucleation barriers at corners for cubic-to-tetragonal phase transformation

We are interested in the energetic cost of a martensitic inclusion of volume $V$ in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of [Kn"upfer, Kohn, Otto: Comm. Pure Appl. Math. 66 (2013), no. 6, 867–904], we consider domain with a corner and obtain a better scaling law for the minimal energy ($E_{min}\sim \min (V^{2\mathrm{/}3},V^{7\mathrm{/}9})$). Our predictions are in a good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.