Regularity for solutions of nonlocal parabolic equations II

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The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, unknown): “See also [8, 55, 83, 101, 121, 219, 233], among many other references.”
Optimal Existence and Uniqueness Theory for the Fractional Heat Equation (2016, background): “in non-divergence form) nonlocal equations we refer to [15, 16] for Hölder continuity results.”
The Schauder estimate for kinetic integral equations (2018, background): “For all r > 0, consider a cut-off function Ψr valued in [0, 1], Ψr ≡ 1 in Br/2 and Ψr ≡ 0 outside Br.”
Schauder estimates for solutions of linear parabolic integro-differential equations (2014, methodology): “|α +|t| α σ ) ≤ 10(c2 +4)γτ−σ. (2.20) Meanwhile, by the Ho¨lder interior estimates, we have that wε 0 locally uniformly converges to some continuous function w. By the stability result Theorem 5.3 in [10], w is a viscosity solution of ∂tw −L0w = f(0,0) in B4 ×(−4σ,−t0] w = w0 in ((Rn \ B4) ×[−4σ,−t0”
Optimal results for the fractional heat equation involving the Hardy potential (2014, methodology): “x0,t0 −h) h + Z Ω u(x0,t0)−u(y,t0) |x−y|N+2s = f(x,t) Therefore, uis a viscosity subsolution. Analogously, we prove that uis a viscosity supersolution. Then we can use the regularity results in [17], [18] and [32]. In particular, by using Corollaries 2.6. 2.7 in [32], for second member Ho¨lder conti”