Weak vector and scalar potentials. Applications to Poincaré's theorem and Korn's inequality in Sobolev spaces with negative exponents.

Chérif Amrouche (1) , Philippe G. Ciarlet (2) , Patrick Ciarlet (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 HKU - Department of Mathematics
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

In this paper, we present several results concerning vector potentials and scalar potentials with data in Sobolev spaces with negative exponents, in a not necessarily simply-connected, three-dimensional domain. We then apply these results to Poincaré's theorem and to Korn's inequality.

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Philippe G. Ciarlet, Patrick Ciarlet. Weak vector and scalar potentials. Applications to Poincaré's theorem and Korn's inequality in Sobolev spaces with negative exponents.. Analysis and Applications, 2010, 8 (1), pp.1-17. ⟨10.1142/s0219530510001497⟩. ⟨hal-00444185⟩