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Mat. Fiz. Anal. Geom., 1996, Volume 3, Number 3/4, Pages 308–331 (Mi jmag499)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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Received: 20.03.1995
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Citation: Niculae Mandache, “On a counterexample concerning unique continuation for elliptic equations in divergence form”, Mat. Fiz. Anal. Geom., 3:3/4 (1996), 308–331

Citation in format AMSBIB
\Bibitem{Man96}
\by Niculae~Mandache
\paper On a counterexample concerning unique continuation for elliptic equations in divergence form
\jour Mat. Fiz. Anal. Geom.
\yr 1996
\vol 3
\issue 3/4
\pages 308--331
\mathnet{http://mi.mathnet.ru/jmag499}


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    This publication is cited in the following articles:
    1. Alessandrini G., Rondi L., Rosset E., Vessella S., “The Stability for the Cauchy Problem for Elliptic Equations”, Inverse Probl., 25:12 (2009), 123004  crossref  mathscinet  zmath  isi  elib
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