On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces
We study the compactness property of the weak convergence in variable Sobolev spaces of the following sequences $\left\{ (A_n,u_n) \in L^1(\Omega; {\mathbb{R}}^{N\times N}) \times W_{A_n}(\Omega; {\Gamma}_D) \right\}$, where the squared symmetric matrices $A\colon \Omega \rightarrow {\mathbb{R}}^{N\...
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2012-08-01
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| Series: | Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika |
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| Online Access: | https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/64 |
| _version_ | 1818998726000115712 |
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| author | P.I. Kogut T.N. Rudyanova |
| author_facet | P.I. Kogut T.N. Rudyanova |
| author_sort | P.I. Kogut |
| collection | DOAJ |
| description | We study the compactness property of the weak convergence in variable Sobolev spaces of the following sequences $\left\{ (A_n,u_n) \in L^1(\Omega; {\mathbb{R}}^{N\times N}) \times W_{A_n}(\Omega; {\Gamma}_D) \right\}$, where the squared symmetric matrices $A\colon \Omega \rightarrow {\mathbb{R}}^{N\times N}$ belong to the Lebesgue space $L^1(\Omega; {\mathbb{R}}^{N\times N})$ and their eigenvalues may vanish on subdomains of $\Omega$ with zero Lebesgue measure. |
| first_indexed | 2024-12-20T22:06:06Z |
| format | Article |
| id | doaj.art-250c93342f834bea941275c8497a14f6 |
| institution | Directory Open Access Journal |
| issn | 2312-9557 2518-7996 |
| language | English |
| last_indexed | 2024-12-20T22:06:06Z |
| publishDate | 2012-08-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika |
| spelling | doaj.art-250c93342f834bea941275c8497a14f62022-12-21T19:25:16ZengOles Honchar Dnipro National UniversityVìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika2312-95572518-79962012-08-0120134144On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev SpacesP.I. Kogut0T.N. Rudyanova1Oles Honchar Dnipropetrovsk National UniversityDnipropetrovsk State Finance AcademyWe study the compactness property of the weak convergence in variable Sobolev spaces of the following sequences $\left\{ (A_n,u_n) \in L^1(\Omega; {\mathbb{R}}^{N\times N}) \times W_{A_n}(\Omega; {\Gamma}_D) \right\}$, where the squared symmetric matrices $A\colon \Omega \rightarrow {\mathbb{R}}^{N\times N}$ belong to the Lebesgue space $L^1(\Omega; {\mathbb{R}}^{N\times N})$ and their eigenvalues may vanish on subdomains of $\Omega$ with zero Lebesgue measure.https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/64matrices with degenerate spectrumweighted Sobolev spacesingular measuresconvergence in variable spaces |
| spellingShingle | P.I. Kogut T.N. Rudyanova On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika matrices with degenerate spectrum weighted Sobolev space singular measures convergence in variable spaces |
| title | On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces |
| title_full | On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces |
| title_fullStr | On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces |
| title_full_unstemmed | On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces |
| title_short | On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces |
| title_sort | on l 1 matrices with degenerate spectrum and weak convergence in associated weighted sobolev spaces |
| topic | matrices with degenerate spectrum weighted Sobolev space singular measures convergence in variable spaces |
| url | https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/64 |
| work_keys_str_mv | AT pikogut onl1matriceswithdegeneratespectrumandweakconvergenceinassociatedweightedsobolevspaces AT tnrudyanova onl1matriceswithdegeneratespectrumandweakconvergenceinassociatedweightedsobolevspaces |