Geodesic
On the Liouville Property for Divergence Form Operators
Canadian journal of mathematics, Tome 50 (1998) no. 3, pp. 487-496

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we construct a bounded strictly positive function $\sigma $ such that the Liouville property fails for the divergence form operator $L\,=\,\nabla ({{\sigma }^{2}}\nabla )$ . Since in addition $\Delta \sigma /\sigma $ is bounded, this example also gives a negative answer to a problem of Berestycki, Caffarelli and Nirenberg concerning linear Schrödinger operators.
DOI : 10.4153/CJM-1998-026-9
Mots-clés : 31C05, 60H10, 35J10 
Barlow, Martin T. On the Liouville Property for Divergence Form Operators. Canadian journal of mathematics, Tome 50 (1998) no. 3, pp. 487-496. doi: 10.4153/CJM-1998-026-9
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