Non-divergence Parabolic Equations of Second Order with Critical Drift in Morrey Spaces
نویسنده
چکیده
We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift −ut + Lu = −ut + ∑ ij aijDiju + ∑ biDiu = 0 (≥ 0, ≤ 0) in some domain Ω ⊂ Rn+1. We prove a variant of Aleksandrov-BakelmanPucci-Krylov-Tso estimate with Lp norm of the inhomogeneous term for some number p < n+1. Based on it, we derive the growth theorems and the interior Harnack inequality. In this paper, we will only assume the drift b is in certain Morrey spaces defined below which are critical under the parabolic scaling but not necessarily to be bounded. This is a continuation of the work in [GC].
منابع مشابه
Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue Spaces
We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift −ut + Lu = −ut + ∑ ij aijDiju + ∑ biDiu = 0 (≥ 0, ≤ 0) in some domain Q ⊂ Rn+1. We prove growth theorems and the interior Harnack inequality as the main results. In this paper, we will only assume the drift b is in certain Lebesgue spaces which are critical under the parabolic scalin...
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