If u(x, y) is an infinity harmonic function, i.e., a viscosity solution to the equation −∆∞u = 0 in Ω ⊂ Rm+1 then the function v(x, z) = u(x, ‖z‖) is infinity harmonic in the set {(x, z) : (x, ‖z‖) ∈ Ω} (provided u(x,−y) = u(x, y)).

We will discuss here Dirichlet problems for non linear …rst order partial di¤erential equations. We will present the recent results of DacorognaMarcellini on this subject; mentioning brie‡y, as a matter of introduction, some results on viscosity solutions.

The stretching response of a single collapsed homopolymer is studied using Brownian dynamic simulations. The irreversibly dissipated work is found to be dominated by internal friction effects below the collapse temperature, and the internal viscosity grows exponentially with the effective cohesive strength between monomers. These results explain friction effects of globular DNA and are relevant...

This article considers the problem of building absolutely minimizing Lipschitz extensions to a given function. These extensions can be characterized as being the solution of a degenerate elliptic partial differential equation, the “infinity Laplacian”, for which there exist unique viscosity solutions. A convergent difference scheme for the infinity Laplacian equation is introduced, which arises...

Most polymers solidify into a glassy amorphous state, accompanied by a rapid increase in the viscosity when cooled below the glass transition temperature (T(g)). There is an ongoing debate on whether the T(g) changes with decreasing polymer film thickness and on the origin of the changes. We measured the viscosity of unentangled, short-chain polystyrene films on silicon at different temperature...

This paper consider various examples of metrics which are contractive w.r.t. an evolution semigroup, and discusses the possibility of an abstract O.D.E. theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced deenition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract ...

We present equilibrium molecular-dynamics computations of the thermal conductivity and the two viscosities of the Yukawa one-component plasma. The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces, and for all the currents which enter the Kubo formulas. For large values of the screening parameter, our estimates of the ...

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = ...

The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as t → ∞ to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied.