The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
نویسندگان
چکیده
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity. While our previous work [IKR] considered the elliptic case, here we treat the more challenging parabolic problem by adapting the classical Moser technique to parabolic equations with drifts with regularity lower than the scale-invariant spaces.
منابع مشابه
The Harnack Inequality for Second-order Elliptic Equations with Divergence-free Drifts
in a domain Ω⊂R. Here a(x) is a given function and b(x) is a prescribed divergence free vector field, i.e., divb=0. The qualitative properties of solutions to elliptic and parabolic equations in divergence form with low regularity of the coefficients have been studied extensively, starting with the classical papers of De Giorgi [5], Nash [12], and Moser [11]. We are mostly interested in the imp...
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