Nonnegative solutions to nonlocal parabolic equations with bounded measurable coefficients are represented exactly by a fundamental solution, with sharp two-sided bounds and new Harnack inequalities.
Time-insensitive nonlocal parabolic Harnack estimates
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abstract
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we show that a waiting-time is required for the nonlocal parabolic Harnack inequality when local solutions are considered.
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Nonnegative solutions to nonlocal parabolic equations
Nonnegative solutions to nonlocal parabolic equations with bounded measurable coefficients are represented exactly by a fundamental solution, with sharp two-sided bounds and new Harnack inequalities.