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Abstract We establish forward, backward and elliptic Harnack inequalities for non-negative solutions to a class of doubly non-linear parabolic partial differential equations.
We establish forward, backward and elliptic Harnack inequalities for non-negative solutions to a class of doubly non-linear parabolic partial differential equations. These Harnack estimates are established in a proper range of parameters p and q below. Such a range is shown to be optimal for a Harnack estimate to hold. Quantitative boundedness estimates for solutions and an expansion of positivity result for non-negative super-solutions are instrumental in the proof.
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Bögelein et al. (2026) studied this question.
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