Abstract
We discuss homogeneous fractional parabolic De Giorgi classes of order s,p and establish the nonlocal weak Harnack estimate with a time gap of order ϱsp, whereas the elliptic case were studied in Cozzi (2017) [4]. The proof relies on a heavy expansion of positivity in the nonlocal framework by-passing the Krylov-Safonov covering argument. Besides, we shall prove the local boundedness and the semicontinuity property. Our results come along with the De Giorgi method.
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