This article is cited in 2 papers

On a counterexample concerning unique continuation for elliptic equations in divergence form

Niculae Mandache

Institut de Mathématiques de Paris Jussieu, CNRS UMR 9994, Equipe de Physique Mathématique et Géométrie, case 7012, Université Paris 7, 2, PL Jussieu, F-75251, Paris Cedex 05, France

Abstract: We construct a second order elliptic equation in divergence form in $\mathrm R^3$, with a non-zero solution which vanishes in a half-space. The coefficients are $\alpha$-Hölder continuous of any order $\alpha<1$. This improves a previous counterexample of Miller [1,2] Moreover, we obtain coefficients which belong to a finer class of smoothness, expressed in terms of the modulus of continuity.

Received: 20.03.1995

Language: English