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arXiv · 2611.03840

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

Serena Dipierro·Ovidiu Savin·Enrico Valdinoci·Riccardo Villa
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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 $L^\infty_{\rm{loc}}$-convergence.

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Serena Dipierro, Ovidiu Savin, Enrico Valdinoci, Riccardo Villa. 2026-11-02. Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates. https://arxiv.org/abs/2611.03840

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