arXiv:2610.37835v1 Announce Type: new Abstract: For every $p > 1$, we establish uniqueness and comparison principle for Trudinger's parabolic equation \[ \partial_t (|u|^{p-2}u) = \text{div}(|\nabla u|^{p-2}\nabla u) \quad \text{in } \Omega \times (0,\text{T}), \] assuming suitable H\"older regularity for the boundary values. Our comparison principle applies to sign-changing weak sub- and supersolutions. As an application, we obtain uniqueness of weak solutions to Cauchy--Dirichlet problems when the lateral boundary data is suitably H\"older continuous in time. In particular, Lipschitz continuous boundary values are covered.
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