Green's Functions and Energy Decay on Homogeneous Spaces

Details Green's Functions and Energy Decay on Homogeneous Spaces Green's Functions and Energy Decay on Homogeneous Spaces

1997-08-09

arxiv.org/abs/funct-an/9708002v2

Physics

Mathematical Physics

To appear in Accademia Nazionale delle Scienze (detta dei XL)

Scientific paper

We consider a homogeneous space X=(X,d,m) of dimension $\nu \geq 1$ and a local regular Dirichlet form in L^{2}(X,m). We prove that if a Poincar\'{e} inequality holds on every pseudo-ball B(x,R) of X, with local characteristic constant c_{0}(x) and c_{1}(r), then a Green's function estimate from above and below is obtained. A Saint-Venant-like principle is recovered in terms of the Energy's decay.

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