Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators
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Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators. / Gimperlein, Heiko; Grubb, Gerd.
In: Journal of Evolution Equations, Vol. 14, 2014, p. 49-83.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators
AU - Gimperlein, Heiko
AU - Grubb, Gerd
PY - 2014
Y1 - 2014
N2 - The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained for perturbations of fractional powers of the Laplacian. In the selfadjoint case, extensions to t∈C+ are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup.
AB - The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained for perturbations of fractional powers of the Laplacian. In the selfadjoint case, extensions to t∈C+ are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup.
U2 - 10.1007/s00028-013-0206-2
DO - 10.1007/s00028-013-0206-2
M3 - Journal article
VL - 14
SP - 49
EP - 83
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
ER -
ID: 95322829