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In this article, we consider the set F of functions annihilated by a uniformly elliptic system S in an open set O of Rn.We show that, as in the case of harmonic functions, F satisfies a submean-property, first for p=2 by elliptic estimates, then for all p > 0:|Nk u(x)|p = C / (rn+kp) ?B(x,r) |u(y)|p dyfor each u in F, each k > 0 and every ball B(x,r) included in O.As a consequence, we can compare ||u||Lp(O) and ||Nku||Lp(O,dkp) where d is the distance to the boundary of O, under the hypothesis that S has constant coefficients or satisfies S(1) = 0.We conclude that, with the metric ||u||Lp(O) + ||Nu||Lp(O) we have a compacity property of the ball of F for all p > 0.

Propriétés de Moyenne pour les solutions de systèmes elliptiques