Solving the biharmonic Dirichlet problem on domains with corners

The biharmonic Dirichlet boundary value problem on a bounded domain is the focus of the present paper. By Riesz' representation theorem the existence and uniqueness of a weak solution is quite direct. The problem that we are interested in appears when one is looking for constructive approximations of a solution. Numerical methods using for example finite elements, prefer systems of second equations to fourth order problems. Ciarlet and Raviart in 7 and Monk in 21 consider approaches through second order problems assuming that the domain is smooth. We will discuss what happens when the domain has corners. Moreover, we will suggest a setting, which is in some sense between Ciarlet‐Raviart and Monk, that inherits the benefits of both settings and that will give the weak solution through a system type approach.     

Sunburn Risk Among Children and Outdoor Workers in South Africa and Reunion Island Coastal Sites

To estimate potential sunburn risk for schoolchildren and outdoor workers, ground‐based ambient solar ultraviolet radiation (UVR) measurements were converted into possible child (5% of ambient solar UVR) and outdoor worker (20% of ambient solar UVR) solar UVR exposures by skin type and season for three coastal sites: Durban, Cape Point (South Africa) and Saint Denis (Reunion Island, France). Cumulative daily ambient solar UVR levels were relatively high at all sites, especially during summer, with maximum values of about 67, 57 and 74 Standard Erythemal Dose (SED) (1 SED = 100 J m^?2) at Durban, Cape Point and Saint Denis respectively. Sunburn risk was evident for both children and outdoor workers, especially those with skin types I and II (extremely to moderately sensitive) during summer, early autumn and/or late spring at all three sites. Although results need to be verified with real‐time, instantaneous and nonintegrated personal solar UVR measurements, this understanding of sunburn risk is useful for initiating the development skin cancer prevention and sun protection awareness campaigns in both countries.