Some remarks on the heat flow for functions
and forms
by Anton Thalmaier
This note is concerned with the differentiation of heat semigroups
on Riemannian manifolds.
In particular, the relation dPtf = Ptdf
is investigated for the semigroup
generated by the Laplacian with Dirichlet boundary conditions.
By means of elementary martingale arguments it is shown that well-known
properties which hold on complete Riemannian manifolds fail if the manifold
is only BM-complete.
Even if M is flat and f smooth of compact support,
the infinity norm of dPtf can in general not be estimated
on compact time intervals in terms of f or df.
Electron. Comm. Probab.
3 (1998) 43-49
https://doi.org/10.1214/ECP.v3-992
The paper is available here:
Anton Thalmaier <anton.thalmaier@uni.lu>
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