Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
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Abstract (arXiv)
We establish a regularity theorem for second-order elliptic PDEs on ℝd 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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 7 of its 23 references that are in the map. First posted on arXiv 22 Feb 2026.
Builds on
7 of 23 references.
References · 7
- 2021Sharp Bounds on the Approximation Rates, Metric Entropy, and n-widths of Shallow Neural Networkscited by 86
- 2020Representation formulas and pointwise properties for Barron functionscited by 62
- 2021Characterization of the Variation Spaces Corresponding to Shallow Neural Networkscited by 48
- 2016Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networkscited by 26
- 2021On the Representation of Solutions to Elliptic PDEs in Barron Spacescited by 25
- 2021A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schr"odinger Eigenvalue Problemscited by 19
- 2025Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditionscited by 1
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Citing papers per year: 2026: 1.
1 paper.