Chapter

# Generalized Hamilton—Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups

• ##### Irina Markina
DOI: 10.1007/978-3-7643-9906-1_3

ABSTRACT We study geometrically invariant formulas for heat kernels of subelliptic differential operators on two step nilpotent Lie
groups and for the Grusin operator in ℝ2. We deduce a general form of the solution to the Hamilton—Jacobi equation and its generalized form in ℝn × ℝm. Using our results, we obtain explicit formulas of the heat kernels for these differential operators.

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