On the Hong–Krahn–Szego inequality for the p-Laplace operator

Given an open set Ω, we consider the problem of providing sharp lower bounds for λ ₂(Ω), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong–Krahn–Szego inequality, asserting that the disjoint unions of two equal balls minimize λ ₂ among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ∞ are considered as well.     

Synthetic Communication: Synthesis of Optically Pure Analogues of D-Arginine Methyl Ester with Antiarrhythmic Activity

The synthesis of the methyl esters of optically pure trans and cis 4-guanidinocyclohexylglycine as rigid analogues of D-arginine methyl ester are described.     

Fluid Flows Around Floating Bodies, I: The Hydrostatic Case

We consider the hydrostatic configuration of a body floating freely on a liquid. Under the influence of gravitational and capillary forces there exists an equilibrium solution with contact angle π/2. This solution is the minimizer of a variational problem with an obstacle condition; the corresponding free boundary consists of the curve where the capillary surface meets the floating body.