Elliptic systems generating a positive semigroup are decoupled
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916964589371392 |
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| author | Arendt, Wolfgang ter Elst, A. F. M. Sauter, Manfred |
| author_facet | Arendt, Wolfgang ter Elst, A. F. M. Sauter, Manfred |
| contents | We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are real-valued. This means the system can be replaced by an equivalent decoupled system (which defines the same semigroup). Instead of matrix coefficients we more generally consider operator-valued coefficients, which leads to interesting additional difficulties with respect to Banach space valued integration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19055 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic systems generating a positive semigroup are decoupled Arendt, Wolfgang ter Elst, A. F. M. Sauter, Manfred Analysis of PDEs Functional Analysis 47A07, 47F10, 35J47, 46G10, 46B42 We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are real-valued. This means the system can be replaced by an equivalent decoupled system (which defines the same semigroup). Instead of matrix coefficients we more generally consider operator-valued coefficients, which leads to interesting additional difficulties with respect to Banach space valued integration. |
| title | Elliptic systems generating a positive semigroup are decoupled |
| topic | Analysis of PDEs Functional Analysis 47A07, 47F10, 35J47, 46G10, 46B42 |
| url | https://arxiv.org/abs/2509.19055 |