AbstractThe singularly perturbed two‐well problem in the theory of solid‐solid phase transitions takes the formwhereu: Ω ⊂ ℝn→ ℝnis the deformation, andWvanishes for all matrices inK= SO(n)A∪ SO(n)B. We focus on the casen= 2 and derive, by means of Gamma convergence, a sharp‐interface limit forIε. The proof is based on a rigidity estimate for low‐energy functions. Our rigidity argument also gives an optimal two‐well Liouville estimate: if ∇uhas a small BV norm (compared to the diameter of the domain), then, in theL1sense, either the distance of ∇ufrom SO(2)Aor the one from SO(2)Bis controlled by the distance of ∇ufromK. This implies that the oscillation of ∇uin weakL1is controlled by theL1norm of the distance of ∇utoK. © 2006 Wiley Periodicals, Inc.