In this paper we prove that a function u ∈ C(Ω) is the continuous value of the Tug-of-War game described in [19] if and only if it is the unique viscosity solution to the infinity laplacian with mixed boundary conditions

This paper is devoted to the study of the maximum principle for the elliptic equation with a deviated argument. We will consider viscosity solutions of this equation.

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This paper presents a mesh quality metric for hexahedral and wedge elements. A series of studies was carried out to relate the proposed metric with the solution errors. During the studies, the metric was also compared with the aspect ratio, the warping factor and the control number. The results show that the metric can be used to identify invalid as well as potential poor quality elements, whic...

In this paper, we investigate the controlled systems described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generator of BSDEs. A new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions. It is worth to pointing out that this theorem has wider applicability...

We report surface rheological measurements on Langmuir films of submicron-sized polymer coils (pancakes). The dynamics of the sol phase is found to be governed by free volume as in the simplest percolation problem. The observed rheology of the percolated phase (gel-like) is compatible with predictions for compressed arrangements of highly deformed soft particles interacting through their contac...

Given a Carnot-Carathéodory metric space (R, dcc) generated by vector fields {Xi} m i=1 satisfying Hörmander’s condition, we prove in theorem A that any absolute minimizer u ∈ W 1,∞ cc (Ω) to F (v,Ω) = supx∈Ω f(x,Xv(x)) is a viscosity solution to the Aronsson equation (1.6), under suitable conditions on f . In particular, any AMLE is a viscosity solution to the subelliptic ∞-Laplacian equation ...

Visible-light-responsive tubular N-doped TiO2 nanocrystallites were synthesized via an environment-conscious solvothermal treatment of protonated titanate nanotubes in an NH4Cl/ethanol/water solution.

• Accuracy. Result is not identical to that of a previous run of the same job, or does not fall within valid range. • Performance. Observe a performance difference from a previous run of the same job. • Portability. Can’t execute the same job on a distinct software stack, platform, or compute site. • Longevity. Unable to reproduce a result due to lack of identical resources as previous run of t...

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)).