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

Yıl 2021, Cilt: 4 Sayı: 1, 93 - 103, 01.03.2021

Simone Ciani Vincenzo Vesprı

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

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

Università degli Studi di Firenze

Teşekkür

Prof. Francesco Altomare.

Kaynakça

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