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

Authors : Simone CİANİ, Vincenzo VESPRI

Pages : 93-103

Doi:10.33205/cma.824336

View : 139 | Download : 13

Publication Date : 2021-03-01

Article Type : Research Paper

Abstract :We give a proof of H ̈older continuity for bounded local weak solutions to the equation ut =\sum_{i=1}^N insert ignore into journalissuearticles values(|u_{x_i}|^{p_i−2} u_{x_i} );_{x_i} , in Ω × [0, T], with Ω ⊂⊂ R^N under the condition 2 < pi < pinsert ignore into journalissuearticles values(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