On recent advances in boundary value problems in the plane
The survey is devoted to recent advances in nonclassical solutions of the main boundary value problems such as the well–known Dirichlet, Hilbert, Neumann, Poincare and Riemann problems in the plane. Such solutions are essentially different from the variational solutions of the classical mathematical...
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| Veröffentlicht in: | Український математичний вісник |
|---|---|
| Datum: | 2016 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/140900 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On recent advances in boundary value problems in the plane / V.Y. Gutlyanskii, V.I. Ryazanov // Український математичний вісник. — 2016. — Т. 13, № 2. — С. 167-212. — Бібліогр.: 76 назв. — рос. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862751005725163520 |
|---|---|
| author | Gutlyanskii, V.Y. Ryazanov, V.I. |
| author_facet | Gutlyanskii, V.Y. Ryazanov, V.I. |
| citation_txt | On recent advances in boundary value problems in the plane / V.Y. Gutlyanskii, V.I. Ryazanov // Український математичний вісник. — 2016. — Т. 13, № 2. — С. 167-212. — Бібліогр.: 76 назв. — рос. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | The survey is devoted to recent advances in nonclassical solutions of the main boundary value problems such as the well–known Dirichlet, Hilbert, Neumann, Poincare and Riemann problems in the plane. Such solutions are essentially different from the variational solutions of the classical mathematical physics and based on the nonstandard point of view of the geometrical function theory with a clear visual sense. The traditional approach of the latter is the meaning of the boundary values of functions in the sense of the so–called angular limits or limits along certain classes of curves terminated at the boundary. This become necessary if we start to consider boundary data that are only measurable, and it is turned out to be useful under the study of problems in the field of mathematical physics, too. Thus, we essentially widen the notion of solutions and, furthermore, obtain spaces of solutions of the infinite dimension for all the given boundary value problems. The latter concerns to the Laplace equation as well as to its counterparts in the potential theory for inhomogeneous and anisotropic media.
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| first_indexed | 2025-12-07T21:09:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-140900 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T21:09:04Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Gutlyanskii, V.Y. Ryazanov, V.I. 2018-07-17T18:59:31Z 2018-07-17T18:59:31Z 2016 On recent advances in boundary value problems in the plane / V.Y. Gutlyanskii, V.I. Ryazanov // Український математичний вісник. — 2016. — Т. 13, № 2. — С. 167-212. — Бібліогр.: 76 назв. — рос. 1810-3200 2010 MSC: 30C62, 30D40, 37E30 https://nasplib.isofts.kiev.ua/handle/123456789/140900 The survey is devoted to recent advances in nonclassical solutions of the main boundary value problems such as the well–known Dirichlet, Hilbert, Neumann, Poincare and Riemann problems in the plane. Such solutions are essentially different from the variational solutions of the classical mathematical physics and based on the nonstandard point of view of the geometrical function theory with a clear visual sense. The traditional approach of the latter is the meaning of the boundary values of functions in the sense of the so–called angular limits or limits along certain classes of curves terminated at the boundary. This become necessary if we start to consider boundary data that are only measurable, and it is turned out to be useful under the study of problems in the field of mathematical physics, too. Thus, we essentially widen the notion of solutions and, furthermore, obtain spaces of solutions of the infinite dimension for all the given boundary value problems. The latter concerns to the Laplace equation as well as to its counterparts in the potential theory for inhomogeneous and anisotropic media. en Інститут прикладної математики і механіки НАН України Український математичний вісник On recent advances in boundary value problems in the plane Article published earlier |
| spellingShingle | On recent advances in boundary value problems in the plane Gutlyanskii, V.Y. Ryazanov, V.I. |
| title | On recent advances in boundary value problems in the plane |
| title_full | On recent advances in boundary value problems in the plane |
| title_fullStr | On recent advances in boundary value problems in the plane |
| title_full_unstemmed | On recent advances in boundary value problems in the plane |
| title_short | On recent advances in boundary value problems in the plane |
| title_sort | on recent advances in boundary value problems in the plane |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140900 |
| work_keys_str_mv | AT gutlyanskiivy onrecentadvancesinboundaryvalueproblemsintheplane AT ryazanovvi onrecentadvancesinboundaryvalueproblemsintheplane |