Compact Embedding Theorem Associated with Classical Weight Functions in Two Variables

M. K. Nangho; B. J. Nkwamouo; J. L. Woukeng

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arXiv · 2605.14732

Compact Embedding Theorem Associated with Classical Weight Functions in Two Variables

M. K. Nangho·B. J. Nkwamouo·J. L. Woukeng

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Abstract

For a classical weight function $\rho$ defined on a simply connected open subset $\Omega$ of $\mathbb{R}^2$ (either bounded or unbounded) with piecewise $C^1$ boundary, we prove density of the space of bivariate polynomials and compact embedding of the matrix-weighted Sobolev space $W^{1,2}(\Omega,\rho,\rho\Phi)$ in the weighted Lebesgue space $L^2(\Omega,\, \rho)$. As an application, we investigate via a variational method, eigenvalue problem for a degenerate Helmholtz operator on triangle.

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BibTeX RIS

M. K. Nangho, B. J. Nkwamouo, J. L. Woukeng. 2026-05-14. Compact Embedding Theorem Associated with Classical Weight Functions in Two Variables. https://arxiv.org/abs/2605.14732

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