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)).

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.

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...

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 ...