# Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates

“Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates” (2026), by Serena Dipierro et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Serena Dipierro, Ovidiu Savin, Enrico Valdinoci, Riccardo Villa
- Published: November 2, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.03840
- Free PDF: https://arxiv.org/pdf/2611.03840

## Abstract

With the aim of extending to parabolic equations the framework developed by the first three authors in [Dipierro, Savin, and Valdinoci, Rev. Mat. Iberoam. (2019)], we introduce a notion of (viscosity) solutions for the space-fractional heat equation modulo k. In turn, we are able to define s-caloric functions with polynomial growth at infinity, showing also related Schauder estimates, a Liouville-type result, and a stability property with respect to the L^∞_loc-convergence.

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