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

2025/07/21 by S. Ciani, Simone Ciani, Ciani, Simone +9 · 1 citation
Mathematics · #35B45 #35B65 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.15730

Abstract

In this paper 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 u_t- ∑_i=1^N D_i(u^2-p_i|D_i u|^p_i-2 D_i u)=0, u\geqslant 0. We prove a parabolic Harnack inequality for nonnegative local weak solutions, without any restrictions on the sparseness of the exponents p_is. Moreover, for a restricted range of diffusion exponents, we prove that solutions are Hölder continuous.

Citations

• Parabolic Harnack Estimates for anisotropic slow diffusion
• Harnack estimates for quasi-linear degenerate parabolic differential equations

Cited by

• The weak Harnack inequality and the rigidity of the anisotropic Trudinger's equation

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