Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces

• URL: http://arxiv.org/abs/2602.19381v1
• Date: Sun, 22 Feb 2026 23:29:57 GMT
• Title: Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
• Authors: Ziang Chen, Liqiang Huang, Mengxuan Yang, Shengxuan Zhou,
• Abstract summary: We establish a regularity theorem for second-order elliptic PDEs on $mathbbRd$ in spectral Barron spaces.<n>We identify a class of PDEs whose solutions can be approximated by two-layer neural networks with cosine activation functions.
• Score: 8.73881274952982
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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