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arXiv · 2510.20432

H\"older regularity for a class of doubly non linear PDEs

Filippo Maria Cassanello·Eurica Henriques
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Abstract

We prove local H\"older continuity for non negative, locally bounded, local weak solutions to the class of doubly nonlinear parabolic equations $\partial_t (u_q) - \text{div} (|Du|^{p-2} Du) = 0$ for $p > 2$, $ 0 < q < p-1$. The proof relies on expansion of positivity results combined with the study of an alternative (related to DeGiorgi-type lemmas) and an exponential shift which allows us to deal with the intrinsic geometry associated to the problem.

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Filippo Maria Cassanello, Eurica Henriques. 2025-10-23. H\"older regularity for a class of doubly non linear PDEs. https://arxiv.org/abs/2510.20432

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