Related papers: Oscillation of H\"older Continuous Functions

We consider one-parameter families of smooth circle cocycles over an ergodic transformation in the base, and show that their rotation numbers must be log-H\"older regular with respect to the parameter. As an immediate application, we get a…

For fractional wave equations with low H\"older regularity damping, we establish quantitative energy decay rates for their solutions when the geometric control condition holds. The energy decay rates depend explicitly on the H\"older…

If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs:…

We investigate the H\"older continuity of solutions to stochastic partial differential equations of the form $\frac{\partial u}{\partial t}=\mathcal{L}u+\sigma(u)\dot{F}$, subject to a suitable initial condition. The noise term $\dot{F}$ is…

We consider a generalized version of the Takagi function, which is one of the most famous example of nowhere differentiable continuous functions. We investigate a set of conditions to describe the rate of convergence of Takagi class…

In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler--Lagrange equations. We show that weak solutions are locally bounded…

We study the class of affine self-similar and continuous on interval $[0;1]$ functions. Formulas for the H\"{o}lder exponents are obtained in terms of self-similarity parameters.

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

We propose an abstract approach to prove local uniqueness and conditional H\"older stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a…

Several versions of It\^{o}'s formula have been obtained in the setting of the functional stochastic calculus. In this regard, we present a local time-space version that works for arbitrary bounded and continuous functionals of L\'{e}vy…

In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear…

The oscillatory behavior of the solutions to a differential equation with several non-monotone delay arguments and non-negative coefficients is studied. A new sufficient oscillation condition, involving lim sup, is obtained. An example…

We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and…

We study the local H\"older regularity of strong solutions $u$ of second-order uniformly elliptic equations having a gradient term with superquadratic growth $\gamma > 2$, and right-hand side in a Lebesgue space $L^q$. When $q >…

We show that oscillations are excited in a complex system under the influence of the external force, if the parameters of the system experience rapid change due to the changes in its internal structure. This excitation is collision-like and…

In this paper we have considered higher order two dimensional coupled system of non-linear ordinary differential equations. We have given necessary and sufficient conditions on the non-linear functions such that the solutions pair oscilla

In this manuscript, we establish asymptotic local exponential stability of the trivial solution of differential equations driven by H\"older--continuous paths with H\"older exponent greater than $1/2$. This applies in particular to…

We prove that bounded harmonic functions of anisotropic fractional Laplacians are H\"older continuous under mild regularity assumptions on the corresponding L\'evy measure. Under some stronger assumptions the Green function, Poisson kernel…

In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…

We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have…