Heat kernel estimates and related inequalities on metric graphs

Sebastian Haeseler

Heat kernel estimates and related inequalities on metric graphs

Mathematical Physics 2011-01-18 v1 math.MP

Authors: Sebastian Haeseler

Abstract

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.

Keywords

metric graphs Kirchhoff boundary conditions heat kernel estimates parabolic Harnack inequality Sobolev inequalities Nash inequalities

Cite

@article{arxiv.1101.3010,
  title  = {Heat kernel estimates and related inequalities on metric graphs},
  author = {Sebastian Haeseler},
  journal= {arXiv preprint arXiv:1101.3010},
  year   = {2011}
}

Comments

20 pages

Related papers

View all related →