Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ? ?ⁿ. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in Ω ×Ω via couplings.

     

Local higher integrability for parabolic quasiminimizers in metric spaces

Using purely variational methods, we prove in metric measure spaces local higher integrability for minimal p-weak upper gradients of parabolic quasiminimizers related to the heat equation. We assume the measure to be doubling and the underlying space to be such that a weak Poincaré inequality is supported. We define parabolic quasiminimizers in the general metric measure space context, and prove an energy type estimate. Using the energy estimate and properties of the underlying metric measure space, we prove a reverse Hölder inequality type estimate for minimal $p$ -weak upper gradients of parabolic quasiminimizers. Local higher integrability is then established based on the reverse Hölder inequality, by using a modification of Gehring’s lemma.     

Determination of retinyl palmitate and total vitamin A content in liver and liver-based ready-to-eat foods.

The determination of retinyl palmitate and total vitamin A in liver and liver-based ready-to-eat foods is described. The method is very simple as sample preparation is minimal, and the isocratic elution of the C18 column with pure methanol does not necessitate a sophisticated instrumental set-up. The method is accurate with high recoveries (100.6 +/- 9.3%, mean +/- S.D., n = 23), and precise with within-day and between-day coefficients of variation of less than 5.5% (n = 13) and less than 16% (n = 6), respectively.     

Reverse Hölder inequalities for singular parabolic equations near the boundary

We show that weak solutions to a singular parabolic partial differential equation globally belong to a higher Sobolev space than assumed a priori. To this end, we prove that the gradients satisfy a reverse Hölder inequality near the boundary. The results extend to singular parabolic systems as well. Motivation for studying reverse Hölder inequalities comes partly from applications to regularity theory.     

Nonlinear parabolic capacity and polar sets of superparabolic functions

We extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the $p$ -Laplacian type. We study definitions and properties of the nonlinear parabolic capacity and show that the capacity of a compact set can be represented via a capacitary potential. As an application, we show that polar sets of superparabolic functions are of zero capacity. The main technical tools used include estimates for equations with measure data and obstacle problems.     

On the magnetovolume effects in YNi3

The thermal expansions of polycrystalline samples of ferromagnetic YNi₃ and paramagnetic YNi₂ have been determined from 4.2 K up to 65 K employing the three-terminal-capacitance method. At low temperatures the expansion of YNi₃ is dominated by a negative magnetic contribution which rapidly vanishes near the Curie temperature. The magnetovolume effects in YNi₃ are discussed within the Stoner-Edwards-Wohlfarth model of very weak itinerant ferromagnetism.