Liqiang Huang

Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces

A regularity theorem is established for second-order elliptic PDEs on $\mathbb{R}^{d}$ in spectral Barron spaces under mild ellipticity and smallness assumptions, and 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...