On Hölder continuity and equivalent formulation of intrinsic Harnack estimates for an anisotropic parabolic degenerate prototype equation

Year 2021, Volume: 4 Issue: 1, 93 - 103, 01.03.2021

Simone Ciani , Vincenzo Vesprı

https://doi.org/10.33205/cma.824336

Cited By: 1

Abstract

We give a proof of H ̈older continuity for bounded local weak solutions to the equation

ut =\sum_{i=1}^N (|u_{x_i}|^{p_i−2} u_{x_i} )_{x_i} , in Ω × [0, T], with Ω ⊂⊂ R^N

under the condition 2 < pi < p(1 + 2/N) for each i = 1, .., N, being p the harmonic mean of the pi's, via
recently discovered intrinsic Harnack estimates. Moreover we establish equivalent forms of these Harnack
estimates within the proper intrinsic geometry.

Keywords

Degenerate Parabolic Equation, Anisotropic, Holder Continuity, Harnack Estimates, Intrinsic Scaling

Supporting Institution

Università degli Studi di Firenze

Thanks

Prof. Francesco Altomare.

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