Symmetry and monotonicity results for positive solutions of p-Laplace systems

We extend to the case of a system involving p-Laplacians, the monotonicity and symmetry results of Damascelli and Pacella obtained in the case of a scalar p-Laplace equation with $1<p<2$. For this purpose, we use the moving hyperplanes method and we suppose that the right hand sides are increasing and locally Lipschitz continuous.Comment: 22 page

A note on the moving hyperplane method

We give more precision on the regularity of the domain that is needed to have the monotonicity and symmetry results recently proved by Damascelli and Pacella, result concerning p-Laplace equations. For this purpose, we study the continuity and semicontinuity of some parameters linked with the moving hyperplane method.Comment: 4 pages, 2 figure

FRAX- vs. T-score-based intervention thresholds for osteoporosis

Many current guidelines for the assessment of osteoporosis, including those in Kuwait, initiate fracture risk assessment in men and women using BMD T-score thresholds. We compared the Kuwaiti guidelines with FRAX-based age-dependent intervention thresholds equivalent to that in women with a prior fragility fracture. FRAX-based intervention thresholds identified women at higher fracture probability than fixed T-score thresholds, particularly in the elderly. PURPOSE: A FRAX® model been recently calibrated for Kuwait, but guidance is needed on how to utilise fracture probabilities in the assessment and treatment of patients. METHODS: We compared age-specific fracture probabilities, equivalent to women with no clinical risk factors and a prior fragility fracture (without BMD), with the age-specific fracture probabilities associated with femoral neck T-scores of -2.5 and -1.5 SD, in line with current guidelines in Kuwait. Upper and lower assessment thresholds for BMD testing were additionally explored using FRAX. RESULTS: When a BMD T-score of -2.5 SD was used as an intervention threshold, FRAX probabilities of a major osteoporotic fracture in women aged 50 years were approximately twofold higher than those in women of the same age but with an average BMD. The increase in risk associated with the BMD threshold decreased progressively with age such that, at the age of 83 years or more, a T-score of -2.5 SD was associated with a lower probability of fracture than that of the age-matched general population with no clinical risk factors. The same phenomenon was observed from the age of 66 years at a T-score of -1.5 SD. A FRAX-based intervention threshold, defined as the 10-year probability of a major osteoporotic fracture in a woman of average BMI with a previous fracture, rose with age from 4.3% at the age of 50 years to 23%, at the age of 90 years, and identified women at increased risk at all ages. Qualitatively comparable findings were observed in the case of hip fracture probability and in men. CONCLUSION: Intervention thresholds based on BMD alone do not optimally target women at higher fracture risk than those on age-matched individuals without clinical risk factors, particularly in the elderly. In contrast, intervention thresholds based on fracture probabilities equivalent to a 'fracture threshold' consistently target women at higher fracture risk, irrespective of age