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Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2010

Lp-Theory for Vector Potentials and Sobolev's Inequalities for Vector Fields

Abstract

In a three dimensional bounded possibly multiply-connected domain, we prove the existence and uniqueness of vector potentials in Lp theory, associated with a divergence-free function and satisfying some boundary conditions. We also present some results concerning scalar potentials and weak vector potentials. Furthermore, variousSobolev-type inequalities are given.
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Dates and versions

hal-00629127 , version 1 (05-10-2011)

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Chérif Amrouche, Nour El Houda Seloula. Lp-Theory for Vector Potentials and Sobolev's Inequalities for Vector Fields. Discrete and Continuous Dynamical Systems - Series S, 2010, 3 (2), pp.159-183. ⟨10.3934/dcdss.2010.3.159⟩. ⟨hal-00629127⟩
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