Green’s Functions and Energy Decay on Homogeneous Spaces
نویسنده
چکیده
We consider a homogeneous space X = (X, d,m) of dimension ν ≥ 1 and a local regular Dirichlet form in L2 (X,m) . We prove that if a Poincaré inequality of exponent 1 ≤ p < ν holds on every pseudo-ball B (x,R) of X, with local characteristic constant c0 (x) and c1 (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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