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October 12, 2025Open Access

Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations

Key Points

Any locally bounded and sign-changing solution is locally Hölder continuous, enhancing understanding of solution behavior.
The proof employs a nonlocal version of De Giorgi technique, showcasing an innovative approach to the regularity problem.
Understanding Hölder regularity for these equations may influence future work on parabolic partial differential equations.
The study reveals local regularity conditions that could apply to various mathematical and physical systems modeled by these equations.

Abstract

We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is equation*split ₜ (|u|^q-1u) +P. V. ₑ䂞|u (x, t) -u (y, t) |^p-2 (u (x, t) -u (y, t) ) |x-y|^{n+sp}\, dy=0, split equation* where 02 and 0<q<p-1. Under a parabolic tail condition, we show that any locally bounded and sign-changing solution is locally Hölder continuous. Our proof is based on a nonlocal version of De Giorgi technique and the method of intrinsic scaling.

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Cite This Study

Qifan Li (Sun,) studied this question.

synapsesocial.com/papers/68ebffcfdef9fcb308ff256b https://doi.org/https://doi.org/10.48550/arxiv.2509.05914