A priori bounds for degenerate and singular evolutionary partial integro-differential equations
The authors study quasilinear evolutionary partial integro-differential equations of second order which include time fractional \(p\)-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique [cf. e.g. \textit{E. Di Benedetto}, Degenerate parabolic equations, New York, NY: Springer-Verlag (1993; Zbl 0794.35090)] they establish results asserting the global boundedness of appropriately defined weak solutions of these problems. It is also showed that a maximum principle is valid for such equations. The authors further prove that in the case of so-called homogeneous structures the weak maximum principle for weak solutions takes the same form as in the classical parabolic case.
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