Boundary Behavior of Non-Negative Solutions of the Heat Equation in Sub-Riemannian Spaces

Details Boundary Behavior of Non-Negative Solutions of the Heat Equation in Sub-Riemannian Spaces Boundary Behavior of Non-Negative Solutions of the Heat Equation in Sub-Riemannian Spaces

2010-05-23

arxiv.org/abs/1005.4239v1

Mathematics

Analysis of PDEs

Scientific paper

We prove Fatou type theorems for solutions of the heat equation in sub-
Riemannian spaces. The doubling property of L-caloric measure, the Dahlberg
estimate, the local comparison theorem, among other results, are established
here. A backward Harnack inequality is proved for non-negative solutions
vanishing in the lateral boundary.

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