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

TL;DR

This paper proves Harnack's estimates for positive solutions of a mixed local and nonlocal doubly nonlinear parabolic equation, providing quantitative bounds and extending classical results to more complex equations.

Contribution

It introduces Harnack's estimates for a new class of mixed local-nonlocal doubly nonlinear parabolic equations with quantitative bounds.

Findings

Established Harnack's estimates for positive solutions

Provided quantitative estimates for the solutions

Extended classical results to mixed local-nonlocal equations

Abstract

We establish Harnack's estimates for positive weak solutions to a mixed local and nonlocal doubly nonlinear parabolic equation. All results presented in this paper are provided together with quantitative estimates.