TY - JOUR

T1 - Analogues of Korn’s Inequality on Heisenberg Groups

AU - Isangulova, D. V.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - Abstract: Two analogues of Korn’s inequality on Heisenberg groups are constructed. First, the norm of the horizontal differential is estimated in terms of its symmetric part. 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 this operator. Additionally, a coercive estimate is proved for a differential operator whose kernel coincides with the Lie algebra of the group of conformal mappings on Heisenberg groups.

AB - Abstract: Two analogues of Korn’s inequality on Heisenberg groups are constructed. First, the norm of the horizontal differential is estimated in terms of its symmetric part. 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 this operator. Additionally, a coercive estimate is proved for a differential operator whose kernel coincides with the Lie algebra of the group of conformal mappings on Heisenberg groups.

KW - DOMAINS

KW - SPACES

UR - http://www.scopus.com/inward/record.url?scp=85067595205&partnerID=8YFLogxK

U2 - 10.1134/S1064562419020248

DO - 10.1134/S1064562419020248

M3 - Article

AN - SCOPUS:85067595205

VL - 99

SP - 181

EP - 184

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -