Author

Mengxuan Yang

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Preprint Aug 2026

Band edges of periodic Schr\"odinger operators are generically isolated and nondegenerate

For periodic Schr\"odinger operators $H_V=-\Delta+V$ with bounded real-valued potentials on $\mathbb R^d$ with $d\ge2$, we show that for generic potentials, each endpoint of every spectral gap is attained by a single Bloch band at only finitely many quasimomenta, and has a nondegenerate Hessian at every attaining point...

Zhong-Kai Tao, Mengxuan Yang · 0 citations

#machine learning Feb 2026

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...

Zi-gao Chen, Liqiang Huang, Mengxuan Yang et al. · arXiv.org · 3 citations