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arXiv · 2507.15730

Qualitative properties of solutions to parabolic anisotropic equations: Part II. The anisotropic Trudinger's equation

Simone Ciani·Eurica Henriques·Mariia O. Savchenko·Igor I. Skrypnik
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Abstract

We study the local regularity properties of weak solutions to a special class of anisotropic doubly nonlinear parabolic operators, whose prototype is the anisotropic Trudinger's equation. We prove a parabolic Harnack inequality, valid without any restrictions on the exponents $p_i$s. When the range of diffusion exponents is restricted, solutions are H\"{o}lder continuous.

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Simone Ciani, Eurica Henriques, Mariia O. Savchenko, Igor I. Skrypnik. 2025-07-21. Qualitative properties of solutions to parabolic anisotropic equations: Part II. The anisotropic Trudinger's equation. https://arxiv.org/abs/2507.15730

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