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Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
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 approxim
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