The harnack inequality for second-order elliptic equations with divergence-free drifts

Mihaela Ignatova; Igor Kukavica; Lenya Ryzhik

doi:10.4310/CMS.2014.v12.n4.a4

The harnack inequality for second-order elliptic equations with divergence-free drifts

Mihaela Ignatova, Igor Kukavica, Lenya Ryzhik

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b∈L^n/2+δ where δ>0. As an application we provide a one-sided Liouville's theorem provided that b∈L^n/2+δ(ℝⁿ).

Original language	English (US)
Pages (from-to)	681-694
Number of pages	14
Journal	Communications in Mathematical Sciences
Volume	12
Issue number	4
DOIs	https://doi.org/10.4310/CMS.2014.v12.n4.a4
State	Published - 2014

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Drift-diffusion equations
Harnack inequality
Liouville theorem
Regularity

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Cite this

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title = "The harnack inequality for second-order elliptic equations with divergence-free drifts",

abstract = "We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b∈Ln/2+δ where δ>0. As an application we provide a one-sided Liouville's theorem provided that b∈Ln/2+δ(ℝn).",

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AU - Ignatova, Mihaela

AU - Kukavica, Igor

AU - Ryzhik, Lenya

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N2 - We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b∈Ln/2+δ where δ>0. As an application we provide a one-sided Liouville's theorem provided that b∈Ln/2+δ(ℝn).

AB - We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b∈Ln/2+δ where δ>0. As an application we provide a one-sided Liouville's theorem provided that b∈Ln/2+δ(ℝn).

KW - Drift-diffusion equations

KW - Harnack inequality

KW - Liouville theorem

KW - Regularity

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IS - 4

ER -

The harnack inequality for second-order elliptic equations with divergence-free drifts

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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