On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form
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...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2015-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/portal/docs/F903785808/157_1_phys_mat_5.pdf |
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| _version_ | 1850088260129259520 |
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| author | M.M. Karchevsky R.R. Shagidullin |
| author_facet | M.M. Karchevsky R.R. Shagidullin |
| author_sort | M.M. Karchevsky |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-719528bf2fda4854b97da7a91ed7610e |
| institution | DOAJ |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-719528bf2fda4854b97da7a91ed7610e2025-08-20T02:43:03ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982015-03-0115714450On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence FormM.M. Karchevsky0R.R. Shagidullin1Kazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaA 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.https://kpfu.ru/portal/docs/F903785808/157_1_phys_mat_5.pdfboundary value problemtransmission problemgeneralized solvability conditions |
| spellingShingle | M.M. Karchevsky R.R. Shagidullin On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form Учёные записки Казанского университета: Серия Физико-математические науки boundary value problem transmission problem generalized solvability conditions |
| title | On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form |
| title_full | On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form |
| title_fullStr | On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form |
| title_full_unstemmed | On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form |
| title_short | On the Transmission Problem for Second-Order Quasilinear Elliptic Equations in Divergence Form |
| title_sort | on the transmission problem for second order quasilinear elliptic equations in divergence form |
| topic | boundary value problem transmission problem generalized solvability conditions |
| url | https://kpfu.ru/portal/docs/F903785808/157_1_phys_mat_5.pdf |
| work_keys_str_mv | AT mmkarchevsky onthetransmissionproblemforsecondorderquasilinearellipticequationsindivergenceform AT rrshagidullin onthetransmissionproblemforsecondorderquasilinearellipticequationsindivergenceform |