On the Hölder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases
Abstract
We prove the Hölder 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 $$0p-1\quad\text{and}\quad p>2.$$ Our proof uses new versions of the integral Harnack type inequalities for sign-changing solutions.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 16 February 2026
- Language
- EN
- Document type
- Preprint