On the lowest eigenvalue of Laplace operators with mixed boundary conditions

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions

Feeding mice with diets containing mercury-contaminated fish flesh from French Guiana: a model for the mercurial intoxication of the Wayana Amerindians

International audienc

Grand Challenges in global eye health: a global prioritisation process using Delphi method

Background We undertook a Grand Challenges in Global Eye Health prioritisation exercise to identify the key issues that must be addressed to improve eye health in the context of an ageing population, to eliminate persistent inequities in health-care access, and to mitigate widespread resource limitations. Methods Drawing on methods used in previous Grand Challenges studies, we used a multi-step recruitment strategy to assemble a diverse panel of individuals from a range of disciplines relevant to global eye health from all regions globally to participate in a three-round, online, Delphi-like, prioritisation process to nominate and rank challenges in global eye health. Through this process, we developed both global and regional priority lists. Findings Between Sept 1 and Dec 12, 2019, 470 individuals complete round 1 of the process, of whom 336 completed all three rounds (round 2 between Feb 26 and March 18, 2020, and round 3 between April 2 and April 25, 2020) 156 (46%) of 336 were women, 180 (54%) were men. The proportion of participants who worked in each region ranged from 104 (31%) in sub-Saharan Africa to 21 (6%) in central Europe, eastern Europe, and in central Asia. Of 85 unique challenges identified after round 1, 16 challenges were prioritised at the global level; six focused on detection and treatment of conditions (cataract, refractive error, glaucoma, diabetic retinopathy, services for children and screening for early detection), two focused on addressing shortages in human resource capacity, five on other health service and policy factors (including strengthening policies, integration, health information systems, and budget allocation), and three on improving access to care and promoting equity. Interpretation This list of Grand Challenges serves as a starting point for immediate action by funders to guide investment in research and innovation in eye health. It challenges researchers, clinicians, and policy makers to build collaborations to address specific challenge

Explicit exponential decay bounds in quasilinear parabolic problems

This paper deals with classical solutions of some initial boundary value problems involving the quasilinear parabolic equation where are given functions. In the case of one space variable, i.e. when , we establish a maximum principle for the auxiliary function where a is an arbitrary nonnegative parameter. In some cases this maximum principle may be used to derive explicit exponential decay bounds for and . Some extensions in space dimensions are indicated. This work may be considered as a continuation of previous works by Payne and Philippin (Mathematical Models and Methods in Applied Sciences, 5 (1995), 95&#8211;110; Decay bounds in quasilinear parabolic problems, In: Nonlinear Problems in Applied Mathematics, Ed. by T.S. Angell, L. Pamela, Cook, R.E., SIAM, 1997).</p

Lower bound for the lifespan of solutions for a class of fourth order wave equations

This paper deals with blow-up solutions of a class of initial-boundary value problems for a fourth order semilinear wave equation. A lower bound for the lifespan of such solutions is derived