The Stokes and Poisson problem in variable exponent spaces

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur

Ophthalmology

PURPOSE: To investigate systemic and ocular determinants of peripapillary retinal nerve fiber layer thickness (pRNFLT) in the European population. DESIGN: Cross-sectional meta-analysis. PARTICIPANTS: A total of 16 084 European adults from 8 cohort studies (mean age range, 56.9+/-12.3-82.1+/-4.2 years) of the European Eye Epidemiology (E3) consortium. METHODS: We examined associations with pRNFLT measured by spectral-domain OCT in each study using multivariable linear regression and pooled results using random effects meta-analysis. MAIN OUTCOME MEASURES: Determinants of pRNFLT. RESULTS: Mean pRNFLT ranged from 86.8+/-21.4 mum in the Rotterdam Study I to 104.7+/-12.5 mum in the Rotterdam Study III. We found the following factors to be associated with reduced pRNFLT: Older age (beta = -0.38 mum/year; 95% confidence interval [CI], -0.57 to -0.18), higher intraocular pressure (IOP) (beta = -0.36 mum/mmHg; 95% CI, -0.56 to -0.15), visual impairment (beta = -5.50 mum; 95% CI, -9.37 to -1.64), and history of systemic hypertension (beta = -0.54 mum; 95% CI, -1.01 to -0.07) and stroke (beta = -1.94 mum; 95% CI, -3.17 to -0.72). A suggestive, albeit nonsignificant, association was observed for dementia (beta = -3.11 mum; 95% CI, -6.22 to 0.01). Higher pRNFLT was associated with more hyperopic spherical equivalent (beta = 1.39 mum/diopter; 95% CI, 1.19-1.59) and smoking (beta = 1.53 mum; 95% CI, 1.00-2.06 for current smokers compared with never-smokers). CONCLUSIONS: In addition to previously described determinants such as age and refraction, we found that systemic vascular and neurovascular diseases were associated with reduced pRNFLT. These may be of clinical relevance, especially in glaucoma monitoring of patients with newly occurring vascular comorbidities

A Placebo-Controlled Trial of Percutaneous Coronary Intervention for Stable Angina.

Percutaneous coronary intervention (PCI) is frequently performed to reduce the symptoms of stable angina. Whether PCI relieves angina more than a placebo procedure in patients who are not receiving antianginal medication remains unknown. We conducted a double-blind, randomized, placebo-controlled trial of PCI in patients with stable angina. Patients stopped all antianginal medications and underwent a 2-week symptom assessment phase before randomization. Patients were then randomly assigned in a 1:1 ratio to undergo PCI or a placebo procedure and were followed for 12 weeks. The primary end point was the angina symptom score, which was calculated daily on the basis of the number of angina episodes that occurred on a given day, the number of antianginal medications prescribed on that day, and clinical events, including the occurrence of unblinding owing to unacceptable angina or acute coronary syndrome or death. Scores range from 0 to 79, with higher scores indicating worse health status with respect to angina. A total of 301 patients underwent randomization: 151 to the PCI group and 150 to the placebo group. The mean (±SD) age was 64±9 years, and 79% were men. Ischemia was present in one cardiac territory in 242 patients (80%), in two territories in 52 patients (17%), and in three territories in 7 patients (2%). In the target vessels, the median fractional flow reserve was 0.63 (interquartile range, 0.49 to 0.75), and the median instantaneous wave-free ratio was 0.78 (interquartile range, 0.55 to 0.87). At the 12-week follow-up, the mean angina symptom score was 2.9 in the PCI group and 5.6 in the placebo group (odds ratio, 2.21; 95% confidence interval, 1.41 to 3.47; P<0.001). One patient in the placebo group had unacceptable angina leading to unblinding. Acute coronary syndromes occurred in 4 patients in the PCI group and in 6 patients in the placebo group. Among patients with stable angina who were receiving little or no antianginal medication and had objective evidence of ischemia, PCI resulted in a lower angina symptom score than a placebo procedure, indicating a better health status with respect to angina. (Funded by the National Institute for Health and Care Research Imperial Biomedical Research Centre and others; ORBITA-2 ClinicalTrials.gov number, NCT03742050.). [Abstract copyright: Copyright © 2023 Massachusetts Medical Society.

Prevalence of Age-Related Macular Degeneration in Europe: The Past and the Future

Purpose Age-related macular degeneration (AMD) is a frequent, complex disorder in elderly of European ancestry. Risk profiles and treatment options have changed considerably over the years, which may have affected disease prevalence and outcome. We determined the prevalence of early and late AMD in Europe from 1990 to 2013 using the European Eye Epidemiology (E3) consortium, and made projections for the future. Design Meta-analysis of prevalence data. Participants A total of 42 080 individuals 40 years of age and older participating in 14 population-based cohorts from 10 countries in Europe. Methods AMD was diagnosed based on fundus photographs using the Rotterdam Classification. Prevalence of early and late AMD was calculated using random-effects meta-analysis stratified for age, birth cohort, gender, geographic region, and time period of the study. Best-corrected visual acuity (BCVA) was compared between late AMD subtypes; geographic atrophy (GA) and choroidal neovascularization (CNV). Main Outcome Measures Prevalence of early and late AMD, BCVA, and number of AMD cases. Results Prevalence of early AMD increased from 3.5% (95% confidence interval [CI] 2.1%–5.0%) in those aged 55–59 years to 17.6% (95%

A second look on definition and equivalent norms of Sobolev spaces

summary:Sobolev's original definition of his spaces $L^{m,p}(\Omega)$ is revisited. It only assumed that $\Omega\subseteq\Bbb R^n$ is a domain. With elementary methods, essentially based on Poincare's inequality for balls (or cubes), the existence of intermediate derivates of functions $u\in L^{m,p}(\Omega)$ with respect to appropriate norms, and equivalence of these norms is proved

A note on the existence of solutions to the Oseen system in Lipschitz domains

Si dimostra che il sistema di Oseen in un dominio esterno dello spazio ammette una soluzione nell’ipotesi che il dato al bordo sia di quadrato sommabile. Tale risultato si applica poi al problema nonlineare di Navier—Stokes

On the exterior two-dimensional Dirichlet problem for elliptic equations

Si dimostra che il problema di Dirichlet per un’equazione di tipo ellittica in un dominio esterno del piano ammette una soluzione se e solo se i dati al contorno e all’infinito soddisfano un’opportuna condizione di compatibilit

Remarks on uniqueness and stability of weak solutions of strongly nonlinear elliptic equations

SIGLETIB: in RO 236 (11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman