The Helmholtz-Weyl decomposition of \(L^r\) vector fields for two dimensional exterior domains

DOI10.1007/s12220-020-00473-4zbMath1466.35146OpenAlexW3043890249MaRDI QIDQ2024654

Anton Seyfert, Taku Yanagisawa, Senjo Shimizu, Hideo Kozono, Matthias Hieber

Publication date: 4 May 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-020-00473-4

zbMATH Keywords

exterior domainsharmonic vector fieldsHelmholtz-Weyl decompositionstream functions and scalar potentials

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Boundary value problems for second-order elliptic systems (35J57)

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Cites Work

• Multiple integrals in the calculus of variations
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• A characterization of harmonic \(L^r\)-vector fields in two-dimensional exterior domains
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• $L^r$-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains
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