We define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is where 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 where 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. 385–395DOI 10.4171/RLM/711