Related papers: Oscillation of H\"older Continuous Functions
In this paper we study the everywhere H\"oder continuity of the minima of a class of vectorial integral funcionals
A previous paper (arXiv:0902.2773, henceforth referred to as I) considered a general class of problems involving the evolution of large systems of globally coupled phase oscillators. It was shown there that, in an appropriate sense, the…
In this paper, we deal with the growth and oscillation of solutions of higher order linear differential equations. Under the conditions that there exists a coefficient which dominates the other coefficients by its lower $% (\alpha ,\beta…
This paper explores the Law of the Iterated Logarithm (LIL) for $m$-dependent sequences under the framework of sub-linear expectations. We first extend existing LIL results to sequences of independent, non-identically distributed random…
We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also…
The classical motion of a one-dimensional chain of atoms coupled through a specific force function that depends on position shows features very similar to the Wannier-Stark problem of a quantum particle under the combined effects of a…
Coupled relaxation oscillators, realized via chemical or other means, can exhibit a multiplicity of steady states, characterized by spatial patterns resulting from lateral inhibition. We show that perturbation-initiated transformations…
In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…
In this survey we prove H\"older regularity results for viscosity solutions of fully nonlinear nonlocal uniformly elliptic second order differential equations with local gradient terms. This extends the nonlocal counterpart of the work of…
We investigate transverse H\"older regularity of some canonical leaf conjugacies in partially hyperbolic dynamical systems and transverse H\"older regularity of some invariant foliations. Our results validate claims made elsewhere in the…
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property…
The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally…
We introduce isotonic conditional laws (ICL) which extend the classical notion of conditional laws by the additional requirement that there exists an isotonic relationship between the random variable of interest and the conditioning random…
It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.
We show, through analytical theory and rigorous numerical calculations, that optical binding can organize a collection of particles into stable one-dimensional lattice. This lattice, as well as other optically-bound structures, are shown to…
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
The Riccati equation method is used to establish some oscillatory criteria for the second order linear functional - differential equations of multiple terms with locally integrable coefficients. An interval oscillation criterion for the…
We prove local H\"older regularity for a nonlocal parabolic equations of the form \begin{align*} \partial_t u + \text{P.V.}\int_{\mathbb{R}^N} \frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+sp}}\,dy=0, \end{align*} for $p\in…
The paper is concerned with a new approach for the recurrence property of the oscillating process on $\mathbb{Z}$ in Kemperman's sense. In the case when the random walk is ascending on $\mathbb{Z}^-$ and descending on $\mathbb{Z}^+$, we…
A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the…