Galerkin Approximation of the Fractional Hardy Constant

Andreea Dima; Liviu I. Ignat

Galerkin Approximation of the Fractional Hardy Constant

Numerical Analysis 2026-07-29 v1 Analysis of PDEs

Authors: Andreea Dima , Liviu I. Ignat

Abstract

We establish sharp estimates for the discrete optimal constant of the fractional Hardy Inequality in dimension $N\geq 1$ , with fractional exponent $s\in \left(0,\min\left\{1,\frac{N}{2}\right\}\right)$ . The convergence rates that we establish take place for the Galerkin approximation with piecewise linear elements, when the computations are carried out in a bounded, convex and smooth domain containing the origin, for which we employ a quasi-uniform and regular mesh.

Keywords

fractional Hardy inequality Galerkin approximation optimal constant convergence rate finite element method

Cite

@article{arxiv.2607.26830,
  title  = {Galerkin Approximation of the Fractional Hardy Constant},
  author = {Andreea Dima and Liviu I. Ignat},
  journal= {arXiv preprint arXiv:2607.26830},
  year   = {2026}
}