Related papers: Boundary behavior of nonlocal minimal surfaces
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively…
We study the long-time asymptotic behavior of the Sticky Particles dynamics on the real line. The time average of the Sticky Particles Lagrangian map has a limit which arises as a general property of projections onto closed convex cones in…
We study the boundary regularity of almost minimal and quasiminimal sets that satisfy sliding boundary conditions. The competitors of a set $E$ are defined as $F = \varphi_1(E)$, where $\{ \varphi_t \}$ is a one parameter family of…
In this paper we study regularity properties of the free boundary problem from superconductivity close to a fixed boundary. If the origin is a free boundary point, then we show that the free boundary touches the fixed boundary tangentially.
Adsorption to a surface, reversible-binding, and trapping are all prevalent scenarios where particles exhibit "stickiness". Escape and first-passage times are known to be drastically affected, but detailed understanding of this phenomenon…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and…
We give partial boundary regularity for co-dimension one absolutely area-minimizing currents at points where the boundary consists of a sum of $C^{1,\alpha}$ submanifolds, possibly with multiplicity, meeting tangentially, given that the…
We consider Dirichlet Laplacians on straight strips in R^2 or layers in R^3 with a weak local deformation. First we generalize a result of Bulla et al. to the three-dimensional situation showing that weakly coupled bound states exist if the…
We investigate the behavior of rotating incompressible flows near a non-flat horizontal bottom. In the flat case, the velocity profile is given explicitly by a simple linear ODE. When bottom variations are taken into account, it is governed…
Given an axially-symmetric, $(n+1)$-dimensional convex cone $\Omega\subset \mathbb{R}^{n+1}$, we study the stability of the free-boundary minimal surface $\Sigma$ obtained by intersecting $\Omega$ with a $n$-plane that contains the axis of…
The general concern of this paper is the effect of rough boundaries on fluids. We consider a stationary flow, governed by incompressible Navier-Stokes equations, in an infinite domain bounded by two horizontal rough plates. The roughness is…
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…
We have performed molecular dynamics simulations of solid-solid contacts lubricated by a model fluid displaying many of the properties of water, particularly its expansive freezing. Near the region where expansive freezing occurs, the…
We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari's Problem. We obtain existence and regularity results,…
This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and…
We obtain a sharp quantitative isoperimetric inequality for nonlocal $s$-perimeters, uniform with respect to $s$ bounded away from $0$. This allows us to address local and global minimality properties of balls with respect to the…
Topological boundary modes can occur at the spatial interface between a topological and gapped trivial phase and exhibit a wavefunction that exponentially decays in the gap. Here we argue that this intuition fails for a temporal boundary…