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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Main Authors: M.M. Karchevsky, R.R. Shagidullin
Format: Article
Language:English
Published: Kazan Federal University 2015-03-01
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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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.
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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