Calculus of Variations and Geometric Measure Theory
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F. Bigolin - F. Serra Cassano

Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups

created by bigolin on 26 Nov 2009

[BibTeX]

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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