Homogeneous Besov spaces on locally compact Vilenkin groups
Homogeneous subsets of the real line
How smooth is almost every function in a Sobolev space?
We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.
Hurewicz properties, non distinguishing convergence properties and sequence selection properties
Hurewicz scheme
Hydrodynamic limit of a d-dimensional exclusion process with conductances
Fix a polynomial Φ of the form Φ(α) = α + ∑2≤j≤m aj αk=1j with Φ'(1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on , with conductances given by special class of functionsW, is described by the unique weak solution of the non-linear parabolic partial differential equation ∂tρ = ∑d ∂xk ∂Wk Φ(ρ). We also derive some properties of the operator ∑k=1d ...
Hydrodynamical behavior of symmetric exclusion with slow bonds
We consider the exclusion process in the one-dimensional discrete torus with points, where all the bonds have conductance one, except a finite number of slow bonds, with conductance , with . We prove that the time evolution of the empirical density of particles, in the diffusive scaling, has a distinct behavior according to the range of the parameter . If , the hydrodynamic limit is given by the usual heat equation. If , it is given by a parabolic equation involving an operator , where ...
Hyers-Ulam stability of mean value points.
Hyper-extensions of -algebras