Regional Patterns of Late Medieval and Early Modern European Building Activity Revealed by Felling Dates

Although variations in building activity are a useful indicator of societal well-being and demographic development, historical datasets for larger regions and longer periods are still rare. Here, we present 54,045 annually precise dendrochronological felling dates from historical construction timber from across most of Europe between 1250 and 1699 CE to infer variations in building activity. We use geostatistical techniques to compare spatiotemporal dynamics in past European building activity against independent demographic, economic, social and climatic data. We show that the felling dates capture major geographical patterns of demographic trends, especially in regions with dense data coverage. A particularly strong negative association is found between grain prices and the number of felling dates. In addition, a significant positive association is found between the number of felling dates and mining activity. These strong associations, with well-known macro-economic indicators from pre-industrial Europe, corroborate the use of felling dates as an independent source for exploring large-scale fluctuations of societal well-being and demographic development. Three prominent examples are the building boom in the Hanseatic League region of northeastern Germany during the 13th century, the onset of the Late Medieval Crisis in much of Europec. 1300, and the cessation of building activity in large parts of central Europe during armed conflicts such as the Thirty Years’ War (1618–1648 CE). Despite new insights gained from our European-wide felling date inventory, further studies are needed to investigate changes in construction activity of high versus low status buildings, and of urban versus rural buildings, and to compare those results with a variety of historical documentary sources and natural proxy archives.</jats:p

Complete Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions, in UMD Spaces

International audienceIn this paper we prove some new results concerning a complete abstract second-order differential equation with general Robin boundary conditions. The study is developped in UMD spaces and uses the celebrated Dore-Venni Theorem. We prove existence, uniqueness and maximal regularity of the strict solution

Resolution and optimal regularity for a biharmonic equation with impedance boundary conditions and some generalizations

International audienceIn this work, a biharmonic equation with an impedance (non standard) boundary condition and more general equations are considered. The study is performed in the space L^{p}(-1,0 ; X), 10} set in a domain having a thin layer. The limiting problem models, for instance, the bending of a thin plate with a stiffness on a part of its boundary. We build an explicit representation of the solution, then we study its regularity and give a meaning to the non standard boundary condition

Pontryagin's Principle for Time-Optimal Problems

International audienceWe consider time-optimal control problems for semilinear parabolic equations with pointwise state constraints and unbounded controls. A Pontryagin's principle is obtained in nonqualified form without any qualification condition. The terminal time, which is a control variable, satisfies an optimality condition, which seems to be new in the context of control problems for partial differential equations