THE HARNACK INEQUALITY FOR SECOND-ORDER ELLIPTIC EQUATIONS WITH DIVERGENCE-FREE DRIFTS

被引：12

作者：

Ignatova, Mihaela ^{[1
]}

Kukavica, Igor ^{[2
]}

Ryzhik, Lenya ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[2] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2014年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

Harnack inequality; Liouville theorem; regularity; drift-diffusion equations; DIFFUSION;

D O I：

10.4310/CMS.2014.v12.n4.a4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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

引用

页码：681 / 694

页数：14

共 16 条

[1] THE EXPLOSION PROBLEM IN A FLOW
Berestycki, Henri
Kiselev, Alexander
Novikov, Alexei
Ryzhik, Lenya
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 2010, 110 : 31 - 65
[2] THE DE GIORGI METHOD FOR REGULARITY OF SOLUTIONS OF ELLIPTIC EQUATIONS AND ITS APPLICATIONS TO FLUID DYNAMICS
Caffarelli, Luis A.
Vasseur, Alexis F.
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (03): : 409 - 427
[3] Caffarelli LA, 2010, ANN MATH, V171, P1903
[4] Diffusion and mixing in fluid flow
Constantin, P.
Kiselev, A.
Ryzhik, L.
Zlatos, A.
[J]. ANNALS OF MATHEMATICS, 2008, 168 (02) : 643 - 674
[5] De Giorgi E., 1957, Mem. Acad. Sci. Torino. Cl. Sci. Fis. Mat. Nat., V3, P25
[6] Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
Friedlander, Susan
Vicol, Vlad
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2011, 28 (02): : 283 - 301
[7] Giaquinta M., 1993, LECT MATH
[8] Untitled
Han, Q.
Wen, B.
Babitsky, V. I.
Silberschmidt, V. V.
[J]. SHOCK AND VIBRATION, 2011, 18 (1-2) : 1 - 1
[9] Liouville theorems for the Navier-Stokes equations and applications
Koch, Gabriel
Nadirashvili, Nikolai
Seregin, Gregory A.
Sverak, Vladimir
[J]. ACTA MATHEMATICA, 2009, 203 (01) : 83 - 105
[10] Kukavica I, 1999, INDIANA U MATH J, V48, P1057

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