Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation

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