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arXiv · 2602.09906

Regularity for Doubly Nonlinear Equations in the Mixed Regime

Simone Ciani·Eurica Henriques·Mariia Savchenko·Igor I. Skrypnik·Yevgeniia Yevgenieva
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Abstract

We study the local H\"older continuity of nonnegative solutions to doubly nonlinear equations by introducing a new technique that allows us to treat the cases where the equation is both singular and degenerate, up to specific Barenblatt numbers. Our argument relies on a new integral $L^1$-$L^1$ Harnack estimate, of independent interest.

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Simone Ciani, Eurica Henriques, Mariia Savchenko, Igor I. Skrypnik, Yevgeniia Yevgenieva. 2026-02-10. Regularity for Doubly Nonlinear Equations in the Mixed Regime. https://arxiv.org/abs/2602.09906

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