Heat Kernels on Metric Measure Spaces and an Application to Semilinear Elliptic Equations

@inproceedings{Grigoryan2003HeatKO,
  title={Heat Kernels on Metric Measure Spaces and an Application to Semilinear Elliptic Equations},
  author={Alexander Grigor’yan and Hu Jiaxin},
  year={2003}
}
We consider a metric measure space (M, d, μ) and a heat kernel pt(x, y) on M satisfying certain upper and lower estimates, which depend on two parameters α and β. We show that under additional mild assumptions, these parameters are determined by the intrinsic properties of the space (M, d, μ). Namely, α is the Hausdorff dimension of this space, whereas β, called the walk dimension, is determined via the properties of the family of Besov spaces Wσ,2 on M . Moreover, the parameters α and β are… CONTINUE READING
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