An $L^p$-Theory for Time-Periodic Mixed-Order Partial Differential Equations under General Boundary Conditions

What the math gives to ML

The paper develops a constructive representation of mixed temporal-spatial regularity using Newton polygons and anisotropic Fourier weights. Its transferable asset is the ability to encode several competing scaling laws instead of imposing one isotropic smoothness assumption. A practical neural-network adaptation is a spectral regularizer for video models, spatiotemporal neural operators, and world models, with candidate scaling regimes selected manually or learned from data.