TY - JOUR

T1 - Analogs of Korn’s Inequality on Heisenberg Groups

AU - Isangulova, D. V.

N1 - Publisher Copyright: © 2019, Pleiades Publishing, Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We give two analogs of Korn’s inequality on Heisenberg groups. First, the norm of the horizontal differential is estimated in terms of the symmetric part of the differential. Second, Korn’s inequality is treated as a coercive estimate for a differential operator whose kernel coincides with the Lie algebra of the isometry group. For this purpose, we construct a differential operator whose kernel coincides with the Lie algebra of the isometry group on Heisenberg groups and prove a coercive estimate for the operator.

AB - We give two analogs of Korn’s inequality on Heisenberg groups. First, the norm of the horizontal differential is estimated in terms of the symmetric part of the differential. Second, Korn’s inequality is treated as a coercive estimate for a differential operator whose kernel coincides with the Lie algebra of the isometry group. For this purpose, we construct a differential operator whose kernel coincides with the Lie algebra of the isometry group on Heisenberg groups and prove a coercive estimate for the operator.

KW - coercive estimate

KW - Heisenberg group

KW - integral representation formula

KW - Korn inequality

KW - Lie algebra of the isometry group

UR - http://www.scopus.com/inward/record.url?scp=85073255231&partnerID=8YFLogxK

U2 - 10.1134/S0037446619050082

DO - 10.1134/S0037446619050082

M3 - Article

AN - SCOPUS:85073255231

VL - 60

SP - 846

EP - 860

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -