JournalsrlmVol. 26, No. 4pp. 385–395

A Harnack’s inequality and Hölder continuity for solutions of mixed type evolution equations

  • Fabio Paronetto

    Università degli Studi di Padova, Italy
A Harnack’s inequality and Hölder continuity for solutions of mixed type evolution equations cover
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Abstract

We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is μ(x)utΔu=0\mu (x) \frac{\partial u}{\partial t} - \Delta u = 0 where μ\mu can be positive, null and negative, so that elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives Hölder-continuity, in particular in the interface II where μ\mu change sign, and a maximum principle.

Cite this article

Fabio Paronetto, A Harnack’s inequality and Hölder continuity for solutions of mixed type evolution equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 385–395

DOI 10.4171/RLM/711