Galerkin Approximation of the Fractional Sobolev Constant
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913122918334464 |
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| author | Dima, Andreea Ignat, Liviu I. |
| author_facet | Dima, Andreea Ignat, Liviu I. |
| contents | We establish sharp estimates for the discrete optimal constant of the fractional Sobolev inequality in dimension $N\geq 1$, with fractional exponent $s\in (0,\min\{1,N/2\})$. The convergence rates that we establish take place for the Galerkin approximation with piecewise linear elements, when the computations are carried out in the unit ball, for which we employ a quasi-uniform and regular mesh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galerkin Approximation of the Fractional Sobolev Constant Dima, Andreea Ignat, Liviu I. Numerical Analysis Analysis of PDEs Classical Analysis and ODEs 65N30, 46E35 We establish sharp estimates for the discrete optimal constant of the fractional Sobolev inequality in dimension $N\geq 1$, with fractional exponent $s\in (0,\min\{1,N/2\})$. The convergence rates that we establish take place for the Galerkin approximation with piecewise linear elements, when the computations are carried out in the unit ball, for which we employ a quasi-uniform and regular mesh. |
| title | Galerkin Approximation of the Fractional Sobolev Constant |
| topic | Numerical Analysis Analysis of PDEs Classical Analysis and ODEs 65N30, 46E35 |
| url | https://arxiv.org/abs/2605.13347 |