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

2010/05/23 by Isidro H. Munive, Munive, Isidro H
Mathematics · Computer Science · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1005.4239

Abstract

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

Citations

• A new proof of Moser's parabolic harnack inequality using the old ideas of Nash

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