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arXiv · 2108.03878

On the H\"older regularity of signed solutions to a doubly nonlinear equation. Part III

Naian Liao·Leah Schätzler
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Abstract

We establish the local H\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad 1<p<2,\quad 0<p-1<q. \] The proof exploits the space expansion of positivity for the singular, parabolic $p$-Laplacian and employs the method of intrinsic scaling by carefully balancing the double singularity.

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Naian Liao, Leah Schätzler. 2021-08-09. On the H\"older regularity of signed solutions to a doubly nonlinear equation. Part III. https://arxiv.org/abs/2108.03878

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