TY - JOUR
T1 - Hardy inequalities, Rellich inequalities and local Dirichlet forms
AU - Robinson, Derek W.
N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - First, the Hardy and Rellich inequalities are defined for the sub-Markovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy inequality. In addition, the Rellich constant is calculated from the Hardy constant. Thirdly, we establish that the criteria for the Rellich inequality are verified for a large class of weighted second-order operators on a domain Ω ⊆ Rd. The weighting near the boundary ∂Ω can be different from the weighting at infinity. Finally, these results are applied to weighted second-order operators on Rd\{0} and to a general class of operators of Grushin type.
AB - First, the Hardy and Rellich inequalities are defined for the sub-Markovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy inequality. In addition, the Rellich constant is calculated from the Hardy constant. Thirdly, we establish that the criteria for the Rellich inequality are verified for a large class of weighted second-order operators on a domain Ω ⊆ Rd. The weighting near the boundary ∂Ω can be different from the weighting at infinity. Finally, these results are applied to weighted second-order operators on Rd\{0} and to a general class of operators of Grushin type.
UR - http://www.scopus.com/inward/record.url?scp=85047665063&partnerID=8YFLogxK
U2 - 10.1007/s00028-018-0454-2
DO - 10.1007/s00028-018-0454-2
M3 - Article
SN - 1424-3199
VL - 18
SP - 1521
EP - 1541
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 3
ER -