Elliptic systems generating a positive semigroup are decoupled

Fuente: arXiv
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Main Authors: Arendt, Wolfgang, ter Elst, A. F. M., Sauter, Manfred
Format: Preprint
Published: 2025
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_version_ 1866916964589371392
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
id 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