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This paper introduces a novel method to extend the Helmholtz Decomposition to n-dimensional sufficiently smooth and fast decaying vector fields.
“Über die Zerlegung unendlicher Vektorfelder”
Otto Blumenthal · 1905
Earlier work this paper cites.
“On the Fundamental Equations of Electromagnetism”
Walter Hauser · 1970
Earlier work this paper cites.
“Elliptic Partial Differential Equations of Second Order” 224
David Gilbarg and Neil. Trudinger · 1977
Earlier work this paper cites.
“On Helmholtz’s Decomposition Theorem and Poissons’s Equation with an Infinite Domain”
Ton Tran-Cong · 1993
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“Uniqueness and reconstruction for the anisotropic Helmholtz decomposition”
George Dassios and Ismo. Lindell · 2002
Earlier work this paper cites.
“Generalizing Cross Products and Maxwell’s Equations to Universal Extra Dimensions”, 2006
A.. McDavid and C.. McMullen · 2006
Earlier work this paper cites.
“On Helmholtz decompositions and their generalizations-An overview”
Wolfgang Sprössig · 2009
Cited alongside, same era.
“The Helmholtz-Hodge Decomposition—A Survey”
Harsh Bhatia, Gregory Norgard, Valerio Pascucci and Peer-Timo Bremer · 2012
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“Quasi-potential landscape in complex multi-stable systems”
Joseph Zhou, M… Aliyu, Erik Aurell and Sui Huang · 2012
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“Cross product in N Dimensions - the doublewedge product”, 2014
Carlo Gonano and Riccardo Zich · 2014
Cited alongside, same era.
“Helmholtz-Hodge Theorems: Unification of Integration and Decomposition Perspectives”, 2014
Jose. Vargas · 2014
Cited alongside, same era.
“On the Helmholtz Theorem and Its Generalization for Multi-Layers”
Alp Kustepeli · 2016
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“The Laplace Equation”
Dagmar Medková · 2018
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“A Constructive Proof of Helmholtz’s Theorem”
Bernardo De and José. Sabina · 2019
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“Construction of Lyapunov functions using Helmholtz–Hodge decomposition”
Tomoharu Suda · 2019
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“Application of Helmholtz–Hodge decomposition to the study of certain vector fields”
Tomoharu Suda · 2020
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Erhard Glötzl and Oliver Richters · 2021
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“The Helmholtz decomposition revisited”
Dietmar Petrascheck · 2015
Cited alongside, same era.
“Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen.”
Hermann von Helmholtz
Cited in the paper.
“On the Dynamical Theory of Diffraction”
George Stokes
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