A Harnack's inequality for mixed type evolution equations
The author considers a class of evolution equations whose simplest example is \[ \mu(x) \frac{\partial u}{\partial t} = \Delta u \] where \(\mu\) can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. By using suitable homogeneous parabolic De Giorgi classes of order 2, the author proves local boundedness and shows a Harnack inequality which, as by-products, gives a maximum principle and Hölder-continuity, in particular along the interface where \(\mu\) changes sign.
scientific article; zbMATH DE number 6535789
scientific article