A frequency localized maximum principle and its applications to time fractional equations with rough coefficients
Year: 2026
Type: preprint
Abstract: We establish a frequency localized maximum principle for parabolic second-order partial differential equations with the Caputo time fractional derivative $\partial_t^α$ of order $α\in(0,1)$. The leading coefficients are uniformly elliptic, measurable in time, and independent of space. We construct suitable equivalent norms on frequency localized subspaces of $L_\infty(\mathbb{R}^d)$, for which a frequency localized maximum principle holds. The corresponding result may fail in the usual $L_\infty$ norm even for the classical heat equation. As an application, we prove existence, uniqueness, and regularity estimates in Sobolev-Zygmund spaces with Muckenhoupt weights in time for equations with spatially variable coefficients and zero initial data. The coefficients are strongly measurable in time with values in a Hölder-Zygmund space of positive order and uniformly bounded in this space.
Source: arXiv (Cornell University)
Authors: Choi, Jae-Hwan, Ryu, Junhee
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223024377