Geodesic
On a counterexample concerning unique continuation for elliptic equations in divergence form
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 308-331 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{JMAG_1996_3_3_a6,
     author = {Niculae Mandache},
     title = {On a counterexample concerning unique continuation for elliptic equations in divergence form},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {308--331},
     year = {1996},
     volume = {3},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a6/}
}
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Niculae Mandache. On a counterexample concerning unique continuation for elliptic equations in divergence form. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 308-331. http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a6/