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Boundary Behavior of Non-Negative Solutions of the Heat Equation in Sub-Riemannian Spaces (1005.4239v1)
Published 23 May 2010 in math.AP
Abstract: 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.