Heat kernel estimates and related inequalities on metric graphs

Details Heat kernel estimates and related inequalities on metric graphs Heat kernel estimates and related inequalities on metric graphs

2011-01-15

arxiv.org/abs/1101.3010v1

Physics

Mathematical Physics

20 pages

Scientific paper

We consider metric graphs with Kirchhoff boundary conditions. We study the
intrinsic metric, volume doubling and a Poincar\'e inequality. This enables us
to prove a parabolic Harnack inequality. The proof involves various techniques
from the theory of strongly local Dirichlet forms. Along our way we show
Sobolev and Nash type inequalities and related heat kernel estimates.

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