相关论文: Medians, Continuity, and Oscillation

Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…

In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…

This article is the first one in a series of two dealing with the concept of "resonant metalens" we recently introduced [Phys. Rev. Lett. 104, 203901 (2010)]. Here, we focus on the physics of a medium with finite dimensions consisting on a…

In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously…

We study the action of uncentered fractional maximal functions on mean oscillation spaces associated with the dyadic Hausdorff content $\mathcal{H}_{\infty}^{\beta}$ with $0<\beta\leq n$. For $0 < \alpha < n$, we refine existing results…

Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its…

This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…

We define oscillating sequences which include the M\"obius function in the number theory. We also define minimally mean attractable flows and minimally mean-L-stable flows. It is proved that all oscillating sequences are linearly disjoint…

In this note we generate two local median oscillation decompositions of an arbitrary measurable function and discuss some applications to Calder\'{o}n-Zygmund singular integral operators $T$. These applications rely on the inequality…

We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.

We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.

We consider a one-dimensional membrane-in-the-middle model for a cavity that consists of two fixed, perfect mirrors and a mobile dielectric membrane between them that has a constant electric susceptibility. We present a sequence of exact…

We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination…

For distinct points $p$ and $q$ in a two-dimensional Riemannian manifold, one defines their mediatrix $L_{pq}$ as the set of equidistant points to $p$ and $q$. It is known that mediatrices have a cell decomposition consisting of a finite…

We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results…

Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the pseudocritical or special values of the associated…

This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their…

In the present paper, mappings satisfying one modular inequality with respect to cylinders in a space, are considered. Distorting of modulus is majorized by an integral which depends from some locally integrable function. The result on…

The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction…

This paper concerns the evolution of a closed convex hypersurface in ${\mathbb{R}}^{n+1}$, in direction of its inner unit normal vector, where the speed is given by a smooth function depending only on the mean curvature, and satisfies some…