An absorbent sanitary article comprising: - a chassis having a longitudinal axis, two side edges, rear and front waist sections (16, 18), and a crotch section intermediate between the rear and front waist sections (16, 18), 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 (16, 18), wherein said at least one gasketing element has a width in the transverse direction which is less than the width in the transverse direction of the respective rear or front waist section (16, 18) of the chassis, wherein the at least one gasketing element includes two non-elastic outer layers (36, 38) and a transversally stretchable elastic film sandwiched between said two non-elastic outer layers (36, 38), wherein the transversally stretchable elastic film is shorter than the two non-elastic outer layers (36, 38) both in the direction of said longitudinal axis and in a transverse direction orthogonal to the longitudinal axis, 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, two side edges, rear and front waist sections (16, 18), and a crotch section intermediate between the rear and front waist sections (16, 18), 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 (16, 18), wherein said at least one gasketing element has a width in the transverse direction which is less than the width in the transverse direction of the respective rear or front waist section (16, 18) of the chassis, wherein the at least one gasketing element includes two non-elastic outer layers (36, 38) and a transversally stretchable elastic film sandwiched between said two non-elastic outer layers (36, 38), wherein the transversally stretchable elastic film is shorter than the two non-elastic outer layers (36, 38) both in the direction of said longitudinal axis and in a transverse direction orthogonal to the longitudinal axis, 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.