Résumé
To a Coxeter system$(W,S)$(with$S$finite) and a weight function$L : W \to \NM$is associated a partition of$W$into Kazhdan-Lusztig (left, right or two-sided)$L$ -cells. Let$S^\circ = \{s \in S | L(s)=0\}$ ,$S^+=\{s \in S | L(s) > 0\}$and let$C$be a Kazhdan-Lusztig (left, right or two-sided)$L$ -cell. According to the semicontinuity conjecture of the first author, there should exist a positive natural number$m$such that, for any weight function$L' : W \to \NM$such that$L(s^+)=L'(s^+) > m L'(s^\circ)$for all$s^+ \in S^+$and$s^\circ \in S^\circ$ ,$C$is a union of Kazhdan-Lusztig (left, right or two-sided)$L'$ -cells. The aim of this paper is to prove this conjecture whenever$(W,S)$is an affine Weyl group and$C$is contained in the lowest two-sided$L$ -cell.