An absorbent sanitary article comprising: - a chassis having a longitudinal axis (X), two side edges , rear and front waist sections , and a crotch section intermediate between the rear and front waist sections , the chassis including a topsheet having an outer surface which in use is in contact with the user's skin, a backsheet , and an absorbent core set between the topsheet and the backsheet , and - at least one gasketing element applied on the outer surface of the topsheet in at least one of said rear and front waist sections , wherein said at least one gasketing element has a width in the transverse direction (Y) which is less than the width in the transverse direction (Y) of the respective rear or front waist section of the chassis , wherein the at least one gasketing element includes two non-elastic outer layers and a transversally stretchable elastic film sandwiched between said two non-elastic outer layers , wherein the transversally stretchable elastic film is shorter than the two non-elastic outer layers both in the direction of said longitudinal axis (X) and in a transverse direction (Y) orthogonal to the longitudinal axis (X), so that the gasketing element has two non-elastic longitudinal portions and two non-elastic transverse portions forming a non-elastic frame surrounding the transversally stretchable elastic film , and wherein the at least one gasketing element is attached to the chassis along a C-shaped attachment profile including two opposite longitudinal portions and a transverse outer portion , wherein a central inner region of the gasketing element is detached from the outer surface of the topsheet to form a pocket open toward said crotch section . - a chassis having a longitudinal axis (X), two side edges , rear and front waist sections , and a crotch section intermediate between the rear and front waist sections , the chassis including a topsheet having an outer surface which in use is in contact with the user's skin, a backsheet , and an absorbent core set between the topsheet and the backsheet , and - at least one gasketing element applied on the outer surface of the topsheet in at least one of said rear and front waist sections , wherein said at least one gasketing element has a width in the transverse direction (Y) which is less than the width in the transverse direction (Y) of the respective rear or front waist section of the chassis , wherein the at least one gasketing element includes two non-elastic outer layers and a transversally stretchable elastic film sandwiched between said two non-elastic outer layers , wherein the transversally stretchable elastic film is shorter than the two non-elastic outer layers both in the direction of said longitudinal axis (X) and in a transverse direction (Y) orthogonal to the longitudinal axis (X), so that the gasketing element has two non-elastic longitudinal portions and two non-elastic transverse portions forming a non-elastic frame surrounding the transversally stretchable elastic film , and wherein the at least one gasketing element is attached to the chassis along a C-shaped attachment profile including two opposite longitudinal portions and a transverse outer portion , wherein a central inner region of the gasketing element is detached from the outer surface of the topsheet to form a pocket open toward said crotch section . <EOS>