arXiv:1005.4239 Abstract | arXiv Analytics

arXiv:1005.4239 [math.AP]Abstract References Reviews Resources

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

Published 2010-05-23Version 1

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.

Categories: math.AP

Subjects: 35K10, 35B05, 31B25

Keywords: heat equation, non-negative solutions, boundary behavior, sub-riemannian spaces, fatou type theorems

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