On Friedrichs Inequality, Helmholtz Decomposition, Vector Potentials, and the div-curl Lemma

  • Ben SchweizerEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 27)


We study connections between four different types of results that are concerned with vector-valued functions \(u:\varOmega \to \mathbb {R}^3\) of class L2(Ω) on a domain \(\varOmega \subset \mathbb {R}^3\): Coercivity results in H1(Ω) relying on div and curl, the Helmholtz decomposition, the construction of vector potentials, and the global div-curl lemma.


Helmholtz Decomposition Vector Potential Friedrichs Inequality Coercivity Result Coercivity Estimate 
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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikTechnische Universität DortmundDortmundGermany

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