On $$$L^1$$$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces

P.I. Kogut; T.N. Rudyanova

doi:10.15421/241219

On $$$L^1$$$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces

P.I. Kogut (Oles Honchar Dnipropetrovsk National University)
T.N. Rudyanova (Dnipropetrovsk State Finance Academy)

Abstract

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.

Keywords

matrices with degenerate spectrum; weighted Sobolev space; singular measures; convergence in variable spaces

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References

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