Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 3, pp. 308-331
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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/
@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/}
}
TY - JOUR
AU - Niculae Mandache
TI - On a counterexample concerning unique continuation for elliptic equations in divergence form
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 1996
SP - 308
EP - 331
VL - 3
IS - 3
UR - http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a6/
LA - en
ID - JMAG_1996_3_3_a6
ER -
%0 Journal Article
%A Niculae Mandache
%T On a counterexample concerning unique continuation for elliptic equations in divergence form
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 1996
%P 308-331
%V 3
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_1996_3_3_a6/
%G en
%F JMAG_1996_3_3_a6
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.
