01802nas a2200229   4500008004100000245010400041210006900145300001400214490000700228520107100235653001001306653001001316653002901326653001501355653002001370653002501390653001801415100003301433700002001466700002501486856006101511       2015                        eng d00aA compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity0 acompatibleincompatible decomposition of symmetric tensors in Lp   a5217-52300 v383 a<p>In this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 &lt; p &lt; 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015&thinsp;John Wiley &amp; Sons, Ltd.</p>10a35J5810a35Q7410acompatibility conditions10aelasticity10aKorn inequality10astrain decomposition10asubclass74B051 aMaggiani, Giovanni, Battista1 aScala, Riccardo1 aVan Goethem, Nicolas  uhttps://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450