A new proof of the Hölder continuity of solutions to p-Laplace type parabolic equations

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It is a well-known fact that solutions to nonlinear parabolic partial differential equations of p-Laplacian type are Hölder continuous. One of the main features of the proof, as originally given by DiBenedetto and DiBenedetto–Chen, consists in studying separately two cases, according to the size of the solution. Here we present a new proof of the Hölder continuity of solutions, which is based on the ideas used in the proof of the Harnack inequality for the same kind of equations recently given by E. DiBenedetto, U. Gianazza and V. Vespri. Our method does not rely on any sort of alternative, and has a strong geometric character.