Geodesic
On the Solvability of a Boundary-Value Problem for an Elliptic Equation
Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 216-224.

Voir la notice de l'article provenant de la source Math-Net.Ru

Consider a boundary-value problem for a second-order linear elliptic equation in a bounded domain. The coefficient of the required function is nonpositive everywhere in the domain, except for a small neighborhood of an interior point. The following question arises: Under what constraints on this coefficient in the given small domain do the statements on the existence and uniqueness of the solution of the first boundary-value problem remain valid?
Keywords: second-order linear elliptic equation, first boundary-value problem, unique solvability of a boundary-value problem. 
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A. M. Il'in; S. V. Repjevskij. On the Solvability of a Boundary-Value Problem for an Elliptic Equation. Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 216-224. http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a4/

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