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arXiv · 2602.19381

Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces

Ziang Chen·Liqiang Huang·Mengxuan Yang·Shengxuan Zhou
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Abstract

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.

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Ziang Chen, Liqiang Huang, Mengxuan Yang, Shengxuan Zhou. 2026-09-03. Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces. https://arxiv.org/abs/2602.19381

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