On a Counterexample Concerning Unique Continuation for Elliptic Equations in Divergence Form

We construct a second order elliptic equation in divergence form in3, with a nonzero solution which vanishes in a half-space.The coefficients are -Hölder continuous of any order < 1. This improves a previous counterexample of Miller (1972, 1974).Moreover, we obtain coefficients which belong to a finer class ofsmoothness, expressed in terms of the modulus of continuity.