Harnack inequality for doubly nonlinear mixed local and nonlocal parabolic equations

Abstract: In this paper, we establish the Harnack inequality of nonnegative weak solutions to the doubly nonlinear mixed local and nonlocal parabolic equations. This result is obtained by combining a related comparison principle, a local boundedness estimate, and an integral Harnack-type inequality. Our proof is based on the expansion of positivity together with a comparison argument.