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This is a Experimental Study study.

October 12, 2025Open Access

Hölder regularity of weak solutions to nonlocal doubly degenerate parabolic equations

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This study demonstrates Hölder continuity in weak solutions of nonlocal parabolic equations, indicating new regularity results.

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.

Qifan Li (2025) studied this question.

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