Comparison of polynomial matrix differential operators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915832991318016 |
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| author | Curcă, Eduard Raiţă, Bogdan |
| author_facet | Curcă, Eduard Raiţă, Bogdan |
| contents | We characterize matrix polynomials $P,Q$ such that the inequality $$ \left\Vert Q(D)u\right\Vert _{L^{2}}\leq C\left\Vert P(D)u\right\Vert _{L^{2}}\quad\text{for all }u\in C_c^\infty(Ω), $$ holds on bounded open sets $Ω$. We also characterize the operators $P,Q$ for which the linear continuous embedding above is compact, i.e., if $u_n\in C_c^\infty(Ω)$ are such that $(P(D)u_n)_{n\geq 1}$ is bounded in $L^2$, then $(Q(D)u_n)_{n\geq 1}$ is strongly compact in $L^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparison of polynomial matrix differential operators Curcă, Eduard Raiţă, Bogdan Functional Analysis Primary: 35G35, Secondary: 35E20 We characterize matrix polynomials $P,Q$ such that the inequality $$ \left\Vert Q(D)u\right\Vert _{L^{2}}\leq C\left\Vert P(D)u\right\Vert _{L^{2}}\quad\text{for all }u\in C_c^\infty(Ω), $$ holds on bounded open sets $Ω$. We also characterize the operators $P,Q$ for which the linear continuous embedding above is compact, i.e., if $u_n\in C_c^\infty(Ω)$ are such that $(P(D)u_n)_{n\geq 1}$ is bounded in $L^2$, then $(Q(D)u_n)_{n\geq 1}$ is strongly compact in $L^2$. |
| title | Comparison of polynomial matrix differential operators |
| topic | Functional Analysis Primary: 35G35, Secondary: 35E20 |
| url | https://arxiv.org/abs/2603.03747 |