A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS
In this paper we discuss some issues related to Poincar´e’s inequality for a special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2019-09-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
| Subjects: | |
| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/136 |
| _version_ | 1818038470062374912 |
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| author | Peter I. Kogut Olha P. Kupenko Guenter Leugering Yue Wang |
| author_facet | Peter I. Kogut Olha P. Kupenko Guenter Leugering Yue Wang |
| author_sort | Peter I. Kogut |
| collection | DOAJ |
| description | In this paper we discuss some issues related to Poincar´e’s inequality for a
special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties. |
| first_indexed | 2024-12-10T07:43:15Z |
| format | Article |
| id | doaj.art-57cb460d4c764b3297c774d93196a3a1 |
| institution | Directory Open Access Journal |
| issn | 2617-0108 2663-6824 |
| language | English |
| last_indexed | 2024-12-10T07:43:15Z |
| publishDate | 2019-09-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Journal of Optimization, Differential Equations and Their Applications |
| spelling | doaj.art-57cb460d4c764b3297c774d93196a3a12022-12-22T01:57:15ZengOles Honchar Dnipro National UniversityJournal of Optimization, Differential Equations and Their Applications2617-01082663-68242019-09-0127212210.15421/141905128A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORSPeter I. Kogut0Olha P. Kupenko1Guenter Leugering2Yue Wang3Department of Differential Equations, Oles Honchar Dnipro National UniversityInstitute of Applied System Analysis, National Academy of Sciences and Ministry of Education and Science of Ukraine Department of System Analysis and Control, National Mining UniversityDepartment Mathematik Lehrstuhl II University Erlangen-NurmbergDepartment of Mathematics, Friedrich-Alenxander University, Erlangen-NurmbergIn this paper we discuss some issues related to Poincar´e’s inequality for a special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties.https://model-dnu.dp.ua/index.php/SM/article/view/136degenerate equationweighted sobolev spacespoincar´e’s inequality |
| spellingShingle | Peter I. Kogut Olha P. Kupenko Guenter Leugering Yue Wang A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS Journal of Optimization, Differential Equations and Their Applications degenerate equation weighted sobolev spaces poincar´e’s inequality |
| title | A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS |
| title_full | A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS |
| title_fullStr | A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS |
| title_full_unstemmed | A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS |
| title_short | A NOTE ON WEIGHTED SOBOLEV SPACES RELATED TO WEAKLY AND STRONGLY DEGENERATE DIFFERENTIAL OPERATORS |
| title_sort | note on weighted sobolev spaces related to weakly and strongly degenerate differential operators |
| topic | degenerate equation weighted sobolev spaces poincar´e’s inequality |
| url | https://model-dnu.dp.ua/index.php/SM/article/view/136 |
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