Geodesic
On the transmission problem for second-order quasilinear elliptic equations in divergence form
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 44-50 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A statement of the transmission problem for quasilinear elliptic equations in divergence form in bounded composed domains in terms of the strengthened Sobolev spaces is proposed. Some generalized sufficient solvability conditions for the Dirichlet boundary value problem are obtained. A condition for which the “flow” is uniquely determined by the solution of the problem is derived. It is noted that the results of this study can be applied for investigations of nonlinear seepage theory problems in composed domains.
Keywords: boundary value problem, generalized solvability conditions.
Mots-clés : transmission problem 
@article{UZKU_2015_157_1_a4,
     author = {M. M. Karchevsky and R. R. Shagidullin},
     title = {On the transmission problem for second-order quasilinear elliptic equations in divergence form},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {44--50},
     year = {2015},
     volume = {157},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a4/}
}
TY  - JOUR
AU  - M. M. Karchevsky
AU  - R. R. Shagidullin
TI  - On the transmission problem for second-order quasilinear elliptic equations in divergence form
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2015
SP  - 44
EP  - 50
VL  - 157
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a4/
LA  - ru
ID  - UZKU_2015_157_1_a4
ER  - 
%0 Journal Article
%A M. M. Karchevsky
%A R. R. Shagidullin
%T On the transmission problem for second-order quasilinear elliptic equations in divergence form
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2015
%P 44-50
%V 157
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a4/
%G ru
%F UZKU_2015_157_1_a4
M. M. Karchevsky; R. R. Shagidullin. On the transmission problem for second-order quasilinear elliptic equations in divergence form. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 44-50. http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a4/

[1] Borsuk M. V., “Apriornye otsenki razreshimost kvazilineinykh ellipticheskikh uravnenii 2-go poryadka v sostavnoi oblasti s nelineinym kraevym usloviem i usloviem sopryazheniya”, Trudy Matem. in-ta AN SSSR, 103, 1968, 15–50 | MR | Zbl

[2] Carstensen C., Funken S. A., “Coupling of nonconforming finite elements and boundary elements. I: A priori estimates”, Computing, 62:3 (1999), 229–241 | DOI | MR | Zbl

[3] Carstensen C., Funken S. A., “Coupling of nonconforming finite elements and boundary elements. II: A posteriori estimates and adaptive mesh-refinement”, Computing, 62:3 (1999), 243–259 | DOI | MR | Zbl

[4] Gatica G. N., Meddahi S., “A dual-dual mixed formulation for nonlinear exterior transmission problems”, Math. Comp., 70:236 (2001), 1461–1480 | DOI | MR | Zbl

[5] Gimperlein H., Maischak M., Schrohe E., Stephan E. P., “Adaptive FE–BE coupling for strongly nonlinear transmission problems with Coulomb friction”, Numer. Math., 117:2 (2011), 307–332 | DOI | MR | Zbl

[6] Dyakonov E. G., “Usilennye prostranstva Soboleva i nekotorye novye tipy ellipticheskikh kraevykh zadach”, Differents. uravneniya, 33:4 (1997), 532–539 | MR | Zbl

[7] Timerbaev M. R., “Prostranstva s normoi grafika i usilennye prostranstva Soboleva. I”, Izv. vuzov. Matem., 2003, no. 5, 55–65 | MR | Zbl

[8] Timerbaev M. R., “Prostranstva s normoi grafika i usilennye prostranstva Soboleva. II”, Izv. vuzov. Matem., 2003, no. 9, 46–53 | MR | Zbl

[9] Yakovlev G. N., “Svoistva reshenii odnogo klassa kvazilineinykh ellipticheskikh uravnenii vtorogo poryadka v divergentnoi forme”, Trudy Matem. in-ta AN SSSR, 131, 1974, 232–242 | MR | Zbl

[10] Lyashko A. D., Karchevskii M. M., “O reshenii nekotorykh nelineinykh zadach teorii filtratsii”, Izv. vuzov. Matem., 1975, no. 6, 73–81 | MR | Zbl

[11] Vainberg M. M., Variatsionnyi metod i metod monotonnykh operatorov, Nauka, M., 1972, 416 pp. | MR

[12] Nečas J., Direct Methods in the Theory of Elliptic Equations, Springer, Berlin–Heidelberg, 2012, 388 pp. | MR

[13] Katorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977, 744 pp. | MR