Related papers: Non-local distance functions and geometric regular…
We investigate the following mixed local and nonlocal quasilinear equation with singularity given by \begin{eqnarray*} \begin{split} -\Delta_pu+(-\Delta)_q^s u&=\frac{f(x)}{u^{\delta}}\text { in } \Omega, \\u&>0 \text{ in } \Omega,\\u&=0…
In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…
We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…
In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
In the present paper, we show that for an optimal class of elliptic operators with non-smooth coefficients on a 1-sided Chord-Arc domain, the boundary of the domain is uniformly rectifiable if and only if the Green function $G$ behaves like…
Background: Functional connectomes (FCs), have been shown to provide a reproducible individual fingerprint, which has opened the possibility of personalized medicine for neuro/psychiatric disorders. Thus, developing accurate ways to compare…
Recent research has shown that piecewise smooth (PS) functions can be approximated by piecewise linear functions with second order error in the distance to a given reference point. A semismooth Newton type algorithm based on successive…
We apply upper and lower compensated convex transforms, which are `tight' one-sided approximations of a given function, to the extraction of fine geometric singularities from semiconvex/semiconcave functions and DC-functions in…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
We introduce a novel class of non-stationary covariance functions for random fields on linear networks that allows both the variance and the correlation range of the random field to vary spatially. The proposed covariance functions are…
In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals in the independent variables. The notion of strong…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-derivative of the cost function by employing the averaged adjoint…
Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…
The persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer was recently generalized by Patel to the case of constructible persistence modules with values in a symmetric monoidal category with images. Patel also introduced a distance…
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of $n-1$ dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys…
In the Engel group with its Carnot group structure we study subsets of locally finite subRiemannian perimeter and possessing constant subRiemannian normal. We prove the rectifiability of such sets: more precisely we show that, in some…