[Théorie
In a three-dimensional bounded possibly multiply-connected domain, we prove the existence and uniqueness of vector potentials in
Dans un ouvert borné tridimensionnel, éventuellement multiplement connexe, nous prouvons lʼexistence et lʼunicité des potentiels vecteurs en théorie
Accepté le :
Publié le :
Chérif Amrouche 1 ; Nour El Houda Seloula 1, 2
@article{CRMATH_2011__349_9-10_529_0, author = {Ch\'erif Amrouche and Nour El Houda Seloula}, title = {$ {L}^{p}$-theory for vector potentials and {Sobolev's} inequalities for vector fields}, journal = {Comptes Rendus. Math\'ematique}, pages = {529--534}, publisher = {Elsevier}, volume = {349}, number = {9-10}, year = {2011}, doi = {10.1016/j.crma.2011.04.008}, language = {en}, }
TY - JOUR AU - Chérif Amrouche AU - Nour El Houda Seloula TI - $ {L}^{p}$-theory for vector potentials and Sobolevʼs inequalities for vector fields JO - Comptes Rendus. Mathématique PY - 2011 SP - 529 EP - 534 VL - 349 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2011.04.008 LA - en ID - CRMATH_2011__349_9-10_529_0 ER -
Chérif Amrouche; Nour El Houda Seloula. $ {L}^{p}$-theory for vector potentials and Sobolevʼs inequalities for vector fields. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 529-534. doi : 10.1016/j.crma.2011.04.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.008/
[1] Vector potentials in three-dimensional nonsmooth domains, Math. Methods Appl. Sci., Volume 21 (1998), pp. 823-864
[2] Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J., Volume 119 (1994) no. 44, pp. 109-140
[3] C. Amrouche, N. Seloula,
[4] A remark on the regularity of solutions of Maxwellʼs equations on Lipschitz domains, Math. Methods Appl. Sci. Theory, Volume 12 (1990), pp. 365-368
[5] Finite Element Methods for the Navier–Stokes Equations, Theory and Algorithms, Springer, Berlin, 1986
[6] Estimating ∇u by div u,
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