In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...

A dilation equation is a functional equation of the form f (t) = N k=0 c k f (2t − k), and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Hölder exponent of continuity of any continuous, compactly supported s...

In this paper, we consider an energy of the type Dirichlet energy plus potential term, for a map with values into a metric cone. We investigate the regularity of minimizers of such functionals, and prove that they are always locally Hölder continuous. We establish that Lipschitz continuity is achieved in some cases where the target space has non-positive curvature, and show examples for which t...

A five-point binary subdivision scheme with a parameter u is presented. The generating polynomial method and the Hölder exponent are used to investigate the uniform convergence and C continuity of this subdivision scheme, where k depends on the choice of the parameter u. Moreover, the conditions on the initial points are discussed for the given limit curve to be convexity preserving and an exam...

Hölder continuity, |Nλ(E) − Nλ(E )| ≤ C|E − E|, with a constant C independent of the disorder strength λ is proved for the integrated density of states Nλ(E) associated to a discrete random operator H = Ho + λV consisting of a translation invariant hopping matrix Ho and i.i.d. single site potentials V with an absolutely continuous distribution, under a regularity assumption for the hopping term.

Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation F (x, u,▽u,▽u) = 0, we establish the interior C continuity under the assumptions that F is uniformly elliptic, Hölder continuous and satisfies the natural structure conditions of fractional order, but without the concavity assumption of F . These assumptions are weaker and the result is stronge...

Abstract. We consider the non-linear equation Tu+∂tu−∂ xπ(u) = ξ driven by space-time white noise ξ, which is uniformly parabolic because we assume that π′ is bounded away from zero and infinity. Under the further assumption of Lipschitz continuity of π′ we show that the stationary solution is — as for the linear case — almost surely Hölder continuous with exponent α for any α < 1 2 w. r. t. th...

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is eleme...

We consider a family of degenerate elliptic equations of the form div(∇F (∇u)) = f , where F ∈ C is a convex function which is elliptic outside a ball. We prove an excess-decay estimate at points where ∇u is close to a nondegenerate value for F . This result applies to degenerate equations arising in traffic congestion, where we obtain continuity of∇u outside the degeneracy, and to anisotropic ...

David and Journé discovered a criterion for the continuity on L of CalderónZygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally Hölder continuous outside the diagonal. The aim of this paper is to prove a David-Journé theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an al...