Geodesic
On the Solvability of a Boundary-Value Problem for an Elliptic Equation
Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 216-224 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_2012_92_2_a4,
     author = {A. M. Il'in and S. V. Repjevskij},
     title = {On the {Solvability} of a {Boundary-Value} {Problem} for an {Elliptic} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {216--224},
     year = {2012},
     volume = {92},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a4/}
}
TY  - JOUR
AU  - A. M. Il'in
AU  - S. V. Repjevskij
TI  - On the Solvability of a Boundary-Value Problem for an Elliptic Equation
JO  - Matematičeskie zametki
PY  - 2012
SP  - 216
EP  - 224
VL  - 92
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a4/
LA  - ru
ID  - MZM_2012_92_2_a4
ER  - 
%0 Journal Article
%A A. M. Il'in
%A S. V. Repjevskij
%T On the Solvability of a Boundary-Value Problem for an Elliptic Equation
%J Matematičeskie zametki
%D 2012
%P 216-224
%V 92
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a4/
%G ru
%F MZM_2012_92_2_a4
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/

[1] A. M. Ilin, Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR | Zbl

[2] A. M. Ilin, “Kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka v oblasti s uzkoi schelyu. 2. Oblast s malym otverstiem”, Matem. sb., 103:2 (1977), 265–284 | MR | Zbl

[3] D. O. Degtyarev, S. V. Repevskii, “Fredgolmovost kraevoi zadachi dlya differentsialnogo uravneniya spetsialnogo vida”, Vestn. Chelyabinsk. gos. un-ta. Ser. Matem. Mekh., 23:12 (2010), 5–11