Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Semi-destructive in situ tests as support to the assessment of a conservation process

This paper refers to the assessment on site by semi-destructive testing (SDT) methods of the consolidation efficiency of a conservation process developed by Henriques (2011) for structural and non-structural pine wood elements in service. This study was applied on scots pine wood (Pinus sylvestris L.) degraded by fungi after treatment with a biocidal product followed by consolidation with a polymeric product. This solution avoids substitutions of wood moderately degraded by fungi, improving its physical and mechanical characteristics. The consolidation efficiency was assessed on site by methods of drill resistance and penetration resistance. The SDT methods used showed good sensitivity to the conservation process and could evaluate their effectiveness. (C) 2015 Elsevier Ltd. All rights reserved.