Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910029906444288 |
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| author | Chen, Ziang Huang, Liqiang Yang, Mengxuan Zhou, Shengxuan |
| author_facet | Chen, Ziang Huang, Liqiang Yang, Mengxuan Zhou, Shengxuan |
| contents | We establish a regularity theorem for second-order elliptic PDEs on $\mathbb{R}^{d}$ in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains two additional orders of Barron regularity. As a corollary, we identify a class of PDEs whose solutions can be approximated by two-layer neural networks with cosine activation functions, where the width of the neural network is independent of the spatial dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces Chen, Ziang Huang, Liqiang Yang, Mengxuan Zhou, Shengxuan Analysis of PDEs Machine Learning Numerical Analysis We establish a regularity theorem for second-order elliptic PDEs on $\mathbb{R}^{d}$ in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains two additional orders of Barron regularity. As a corollary, we identify a class of PDEs whose solutions can be approximated by two-layer neural networks with cosine activation functions, where the width of the neural network is independent of the spatial dimension. |
| title | Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces |
| topic | Analysis of PDEs Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2602.19381 |