منابع مشابه
On Divergence-free Drifts
We investigate the validity and failure of Liouville theorems and Harnack inequalities for parabolic and elliptic operators with low regularity coefficients. We are particularly interested in operators of the form ∂t−∆+ b ·∇ resp. −∆+ b ·∇ with a divergence-free drift b. We prove the Liouville theorem and Harnack inequality when b ∈ L∞(BMO) resp. b ∈ BMO−1 and provide a counterexample demonstra...
متن کاملThe Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
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.
متن کاملThe 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...
متن کاملLocal W -regularity Estimates for Weak Solutions of Parabolic Equations with Singular Divergence-free Drifts
We study weighted Sobolev regularity of weak solutions of nonhomogeneous parabolic equations with singular divergence-free drifts. Assuming that the drifts satisfy some mild regularity conditions, we establish local weighted Lp-estimates for the gradients of weak solutions. Our results improve the classical one to the borderline case by replacing the L∞-assumption on solutions by solutions in t...
متن کاملDivergence-free RBFs on Surfaces∗
This paper presents a new tool for fitting a divergence-free vector field tangent to a two dimensional orientable surface P ∈ R to samples of such a field taken at scattered sites on P . This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the me...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2012
ISSN: 0022-0396
DOI: 10.1016/j.jde.2011.08.039