Harnack's estimate for a mixed local-nonlocal doubly nonlinear parabolic equation (Q2680527)

In this paper, the author establishes Harnack's estimates for positive weak solutions to a mixed local and nonlocal doubly nonlinear parabolic equation, of the type \[ \frac{\partial}{\partial t}(|u|^{p-2}u)-\operatorname{div}A (x, t, u, Du) + Lu(x, t) = 0, \] where the vector field \(A\) satisfies the \(p\)-ellipticity and growth conditions and the integrodifferential operator \(L\) whose model is the fractional \(p\)-Laplacian. Noteworthy is that all the results demonstrated in this paper are provided using sharp estimates in the doubly nonlinear theory together with quantitative estimates.