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

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

Abstract

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.

Keywords

Helmholtz Decomposition Vector Potential Friedrichs Inequality Coercivity Result Coercivity Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikTechnische Universität DortmundDortmundGermany

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