Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials
Fundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built. The basic boundary value problems for a degenerate elliptic equation are reduced to the equivalent Fredholm integral equations of the second kind. Their...
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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/F2130142300/157_1_phys_mat_1.pdf |
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| _version_ | 1841563858359025664 |
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| author | R.M. Askhatov R.N. Abaydullin |
| author_facet | R.M. Askhatov R.N. Abaydullin |
| author_sort | R.M. Askhatov |
| collection | DOAJ |
| description | Fundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built. The basic boundary value problems for a degenerate elliptic equation are reduced to the equivalent Fredholm integral equations of the second kind. Their solvability is proved. |
| format | Article |
| id | doaj-art-912a4a3a37a947869d40e7c6539d0451 |
| institution | Kabale University |
| 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-912a4a3a37a947869d40e7c6539d04512025-01-02T23:25:17ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982015-03-011571514Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of PotentialsR.M. Askhatov0R.N. Abaydullin1Kazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaFundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built. The basic boundary value problems for a degenerate elliptic equation are reduced to the equivalent Fredholm integral equations of the second kind. Their solvability is proved.https://kpfu.ru/portal/docs/F2130142300/157_1_phys_mat_1.pdfdegenerate elliptic equationmethod of potentialsdouble layer potentialsimple layer potentialfredholm equationgeneralized translation operator |
| spellingShingle | R.M. Askhatov R.N. Abaydullin Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials Учёные записки Казанского университета: Серия Физико-математические науки degenerate elliptic equation method of potentials double layer potential simple layer potential fredholm equation generalized translation operator |
| title | Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials |
| title_full | Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials |
| title_fullStr | Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials |
| title_full_unstemmed | Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials |
| title_short | Solution of the Basic Boundary Value Problems for a Degenerate Elliptic Equation by the Method of Potentials |
| title_sort | solution of the basic boundary value problems for a degenerate elliptic equation by the method of potentials |
| topic | degenerate elliptic equation method of potentials double layer potential simple layer potential fredholm equation generalized translation operator |
| url | https://kpfu.ru/portal/docs/F2130142300/157_1_phys_mat_1.pdf |
| work_keys_str_mv | AT rmaskhatov solutionofthebasicboundaryvalueproblemsforadegenerateellipticequationbythemethodofpotentials AT rnabaydullin solutionofthebasicboundaryvalueproblemsforadegenerateellipticequationbythemethodofpotentials |