Compact Embedding Theorem Associated with Classical Weight Functions in Two Variables
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910253353795584 |
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| author | Nangho, M. K. Nkwamouo, B. J. Woukeng, J. L. |
| author_facet | Nangho, M. K. Nkwamouo, B. J. Woukeng, J. L. |
| contents | For a classical weight function $ρ$ defined on a simply connected open subset $Ω$ of $\mathbb{R}^2$ (either bounded or unbounded) with piecewise $C^1$ boundary, we prove density and compact embedding of a matrix-weighted Sobolev space in the weighted Lebesgue space $L^2(Ω,\, ρ)$. As an application, we investigate via a variational method, eigenvalue problem for a degenerate Helmholtz operator on triangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compact Embedding Theorem Associated with Classical Weight Functions in Two Variables Nangho, M. K. Nkwamouo, B. J. Woukeng, J. L. Classical Analysis and ODEs Matrix-weighted sobolev spaces, compact embedding, generalized Helmholtz operator For a classical weight function $ρ$ defined on a simply connected open subset $Ω$ of $\mathbb{R}^2$ (either bounded or unbounded) with piecewise $C^1$ boundary, we prove density and compact embedding of a matrix-weighted Sobolev space in the weighted Lebesgue space $L^2(Ω,\, ρ)$. As an application, we investigate via a variational method, eigenvalue problem for a degenerate Helmholtz operator on triangle. |
| title | Compact Embedding Theorem Associated with Classical Weight Functions in Two Variables |
| topic | Classical Analysis and ODEs Matrix-weighted sobolev spaces, compact embedding, generalized Helmholtz operator |
| url | https://arxiv.org/abs/2605.14732 |