Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation
2021
We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional p-Laplace equation. Our argument relies on energy estimates and a parabolic nonlocal version of De Giorgi’s method. Furthermore, by means of a new algebraic inequality, we show that positive weak supersolutions satisfy a reverse Holder inequality. Finally, we also prove a logarithmic decay estimate for positive supersolutions.
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