*Accepted Paper*

**Inserted:** 26 nov 2009

**Journal:** JMAA

**Pages:** 11

**Year:** 2009

**Abstract:**

In the present paper we will characterize the continuous distributional solutions of Burgers' equation such as those which induce intrinsic regular graphs in the first Heisenberg group $\mathbb H^1\equiv \mathbb R^{3}$, endowed with a left- invariant metric $d_{\infty}$ equivalent to its Carnot- Carathéodory metric. We will also extend the characterization to higher Heisenberg groups $\mathbb H^n\equiv\mathbb R^{2n+1}$.

**Keywords:**
Burgers' equation, Heisenberg group, Carnot-Carathéodory metric, intrinsic graph

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