ensemble J u est l'ensemble des sauts de u : c'est un ensemble H n?1 -rectifiable sur lequel on peut définir H n?1 -p.p. une normale généralisée unitaire, notée ? u , ainsi que des traces supérieures et inférieures u ± . Enfin D c u désigne la partie Cantorienne. On dit que u ? SBV (?; R m ), l'ensemble des fonctions spécialesspécialesà variation bornée ,
espace GSBV (?; R m ) des fonctions spécialesspécialesà variation bornée généralisées défini comme l'ensemble des applications mesurables u : ? ? R m telles que ? ? u ? SBV loc (?; R m ), quelque soit ? ? C 1 (R m ; R m ) tel que supp(??) est compact dans R m . Notons qu'il est toujours possible de définir une notion de gradient approché et d'ensemble de saut pour des fonctions dans cet espace (voir Dal Maso, Pour p > 1, on définit enfin les espaces SBV p (?; R m ) := {u ? SBV (?; R m ) : ?u ? L p (?; M m×n ), H n?1 (J u ) < ?} ,
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