RESUMEN
We prove that each Borel function V : Ω â [ - ∞ , + ∞ ] defined on an open subset Ω â R N induces a decomposition Ω = S ⪠â i D i such that every function in W 0 1 , 2 ( Ω ) â© L 2 ( Ω ; V + d x ) is zero almost everywhere on S and existence of nonnegative supersolutions of - Δ + V on each component D i yields nonnegativity of the associated quadratic form ∫ D i ( | ∇ ξ | 2 + V ξ 2 ) . .
RESUMEN
In this paper we study the regularity and the behavior in time of the solutions to a quasilinear class of noncoercive problems whose prototype is u t - div ( a ( x , t , u ) ∇ u ) = - div ( u E ( x , t ) ) in Ω × ( 0 , T ) , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω . In particular we show that under suitable conditions on the vector field E, even if the problem is noncoercive and although the initial datum u 0 is only an L 1 ( Ω ) function, there exist solutions that immediately improve their regularity and belong to every Lebesgue space. We also prove that solutions may become immediately bounded. Finally, we study the behavior in time of such regular solutions and we prove estimates that allow to describe their blow-up for t near zero.
RESUMEN
BACKGROUND: Locking plates are the gold standard for treatment of 3-part humeral head fractures, although major complications range from 9% to 36%. Percutaneous techniques may allow vascular supply preservation, maintenance of fracture hematoma, scarce blood loss. Many configurations with Kirschner wires can be performed, generating confusion on result interpretation. We studied the correlation between system configuration, stability, and clinical results in patients with 3-part humeral head fractures treated with the same fixation system but with 2 different biomechanical constructs. MATERIALS AND METHODS: There were 52 consecutive patients (19 men, 33 women; mean age, 63.1 [standard deviation, 5.6] years; range, 48-82 years) with Hertel 7 humeral head fractures. Two fixation constructs composed of 3 couples (construct A) or 4 couples (construct B) of blocked threaded wires were used in 17 and 35 patients, respectively. At the final follow-up, the individual relative Constant Score (irCS) and visual analog scale were measured. Radiographic evaluation according to the Bahr criteria was performed. Statistical analysis was performed. RESULTS: The mean follow-up was 22 months. The mean irCS at the final follow-up was 89.7%. The mean irCS in patients treated with construct A and construct B was 86% and 93%, respectively (P = .043). One nonunion and 2 superficial infections occurred (6%). The postoperative reduction was excellent in 97% of patients and remained excellent in 89%. The mean postoperative neck shaft angle was 135.0° (construct A: 134.7°; construct B: 135.1°), and the final neck shaft angle was 132.9° (construct A: 131.3°; construct B: 133.8°; P = .047). CONCLUSIONS: The functional and radiologic outcomes obtained with percutaneous fixation or locking plates are similar; however, the percentage of major complications after percutaneous treatment is lower. Results of percutaneous fixation depend on the biomechanical construct.
