On the H\"{o}lder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases

Igor I. Skrypnik

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arXiv · 2602.14800

On the H\"{o}lder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases

Igor I. Skrypnik

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Abstract

We prove the H\"{o}lder continuity of sign-changing solutions to the equation of the type $$\frac{\partial}{\partial t}\big(|u|^{q-1} u\big)- div\Big(|D u|^{p-2}\,D u\Big)=0,$$ where numbers $p$, $q$ satisfy the conditions $$0 p-1\quad\text{and}\quad p>2.$$ Our proof uses new versions of the integral Harnack type inequalities for sign-changing solutions.

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Igor I. Skrypnik. 2026-02-16. On the H\"{o}lder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases. https://arxiv.org/abs/2602.14800

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