Pseudo-differential equations and conical potentials: 2-dimensional case
We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and th...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2019-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol39/1/art/opuscula_math_3908.pdf |
| _version_ | 1819081653026291712 |
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| author | Vladimir B. Vasilyev |
| author_facet | Vladimir B. Vasilyev |
| author_sort | Vladimir B. Vasilyev |
| collection | DOAJ |
| description | We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given. |
| first_indexed | 2024-12-21T20:04:11Z |
| format | Article |
| id | doaj.art-1288bab8470d4d65a39017c49a92e363 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-21T20:04:11Z |
| publishDate | 2019-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-1288bab8470d4d65a39017c49a92e3632022-12-21T18:51:54ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01391109124https://doi.org/10.7494/OpMath.2019.39.1.1093908Pseudo-differential equations and conical potentials: 2-dimensional caseVladimir B. Vasilyev0https://orcid.org/0000-0001-9351-8084Chair of Differential Equations, Belgorod National Research State University, Studencheskaya 14/1, Belgorod 308007, RussiaWe consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.https://www.opuscula.agh.edu.pl/vol39/1/art/opuscula_math_3908.pdfpseudo-differential equationwave factorizationdirichlet problemsystem of linear integral equations |
| spellingShingle | Vladimir B. Vasilyev Pseudo-differential equations and conical potentials: 2-dimensional case Opuscula Mathematica pseudo-differential equation wave factorization dirichlet problem system of linear integral equations |
| title | Pseudo-differential equations and conical potentials: 2-dimensional case |
| title_full | Pseudo-differential equations and conical potentials: 2-dimensional case |
| title_fullStr | Pseudo-differential equations and conical potentials: 2-dimensional case |
| title_full_unstemmed | Pseudo-differential equations and conical potentials: 2-dimensional case |
| title_short | Pseudo-differential equations and conical potentials: 2-dimensional case |
| title_sort | pseudo differential equations and conical potentials 2 dimensional case |
| topic | pseudo-differential equation wave factorization dirichlet problem system of linear integral equations |
| url | https://www.opuscula.agh.edu.pl/vol39/1/art/opuscula_math_3908.pdf |
| work_keys_str_mv | AT vladimirbvasilyev pseudodifferentialequationsandconicalpotentials2dimensionalcase |