A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I.

We continue the study of the space  B V α ( R n ) of functions with bounded fractional variation in  R n of order α ∈ ( 0 , 1 ) introduced in our previous work (Comi and Stefani in J Funct Anal 277(10):3373-3435, 2019). After some technical improvements of certain results of Comi and Stefani (2019) which may be of some separated insterest, we deal with the asymptotic behavior of the fractional operators involved as α → 1 - . We prove that the α -gradient of a W 1 , p -function converges in L p to the gradient for all p ∈ [ 1 , + ∞ ) as α → 1 - . Moreover, we prove that the fractional α -variation converges to the standard De Giorgi's variation both pointwise and in the Γ -limit sense as α → 1 - . Finally, we prove that the fractional ß -variation converges to the fractional α -variation both pointwise and in the Γ -limit sense as ß â†’ α - for any given α ∈ ( 0 , 1 ) .

Plastic Biliary Stent Migration During Multiple Stents Placement and Successful Endoscopic Removal Using Intra-Stent Balloon Inflation Technique: A Case Report and Literature Review.

BACKGROUND: Late migration of a plastic biliary stent after endoscopic placement is a well known complication, but there is little information regarding migration of a plastic stent during multiple stents placement. CASE REPORT: A white man was hospitalized for severe jaundice due to neoplastic hilar stenosis. Surgical eligibility appeared unclear on admission and endoscopy was carried out, but the first stent migrated proximally at the time of second stent insertion. After failed attempts with various devices, the migrated stent was removed successfully through cannulation with a dilation balloon. CONCLUSIONS: The migration of a plastic biliary stent during multiple stents placement is a possible complication. In this context, extraction can be very complicated. In our patient, cannulation of a stent with a dilation balloon was the only effective method.

Large Bowel Obstruction Due to a Big Gallstone Successfully Treated with Endoscopic Mechanical Lithotripsy.

Colonic gallstone ileus in an uncommon mechanical bowel obstruction caused by intraluminal impaction of one or more gallstones. The surgical management of gallstone ileus is complex and is potentially of high risk. There have been reports of gallstone extractions using various endoscopic modalities to relieve the obstruction. In this report we present the technique employed to successfully perform a mechanical lithotripsy and extraction of a large gallstone embedded in a sigmoid colon affected by diverticular stenosis. We passed through the stenosis with a 11.3 mm videoscope with 3.7 mm channel. A large lithotripsy extraction basket was used to catch and break up the stone and fragments were removed using the same basket. The patient was discharged asymptomatic three days after the procedure. Using appropriate devices mechanical lithotripsy is a safe and effective method to treat colonic obstruction and avoid surgery in the setting of gallstone ileus even in case of big stones.