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\...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Oles Honchar Dnipro National University
2012-08-01
|
| Series: | Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika |
| Subjects: | |
| Online Access: | https://vestnmath.dnu.dp.ua/index.php/dumb/article/view/64 |
| Summary: | 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. |
|---|---|
| ISSN: | 2312-9557 2518-7996 |