In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of the dispersed phase species from one emulsion droplet (or foam bubble) to another. Previous studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can overcome the Laplace pressure differences that drive coarsening, and " osmotically stabilise ...

preprint numerics no. 2/2007 norwegian university of science and technology trondheim, norway The 'pseudo-harmonic' extension is an approximation to the common harmonic extension for extending a function over a domain based on its trace along the boundary of the domain. On a circle the two extension methods produce identical results. We present explicit formulas for the computation of distance ...

Generalization of the harmonic superposition rule for the case of dependent choice of harmonic functions is given. Dependence of harmonic functions from all (relative and overall) transverse coordinates is considered using the BeltramiLaplace operator. Supersymmetry of IIB 10D supergravity solutions with only non-vanished 5-form field and 11D supergravity solutions is discussed.

There are proven generalizations of the Hölder's and Minkowski's inequalities for the pseudo-integral. There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g, the second semiring ([a, b], sup,), where is generated and the third semiring where both pseudo-operations are idempotent, i.e., È = sup an...

We describe the role of p-harmonic functions in the theory of quasiregular mappings.

We consider the p–Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p → ∞.

We study the enclosure method for the p-Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, wh...

The purpose of this paper is to give some geometric results on the following problem: −div ( α(x)|∇u(X)|p(x)−2∇u(X) ) = f(x, u(X)) in Ω, (1.1) where f = f(x, u) ∈ L∞(Rm×R) is differentiable in u with fu ∈ L∞(R), α ∈ L∞(Rm), with inf Rm α > 0, p ∈ L∞(Rm), with p(x) ≥ 2 for any x ∈ R, and Ω is an open subset of R. Here, u = u(X), with X = (x, y) ∈ R × Rn−m. As well known, the operator in (1.1) co...

Bu araştırmada, başlangıç değer koşullarına bağlı pseudo-hiperbolik telegraf kısmi diferansiyel denklemi incelendi. problemin tam çözümü için modifiye çift Laplace metodu verildi. metot örnek problemlere uygulanarak çözüm elde edildi. Elde edilen bu simülasyonlarla gösterildi. Böylece metodunun elverişli ve uygun olduğu görüldü.