Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups
type: Item
instance of: scholarly article
title: Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups
zbMATH Open document ID: 1186.35030
author: Francesco Bigolin
author: Francesco Serra Cassano
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-03-29T00:00:00Z
review text: The authors characterize the continuous distributional solutions of Burgers' equation in an open set in \(\mathbb{R}^2\) as those, which, considered as a graph in the Heisenberg group \(\mathbb{H}^1 = \mathbb{R}^3\) endowed with a left invariant metric \(d_\infty\) equivalent to the Carnot-Carathéodory metric, are intrinsic regular. The characterization is also extended to higher dimensional Heisenberg group \(\mathbb{H}^n = \mathbb{R}^{2n+1}\).
reviewed by: Marco Biroli
Mathematics Subject Classification ID: 35H20
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35R03
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 5687660
zbMATH Keywords: Burgers' equation
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Carnot Carathéodory metric
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.11.042
OpenAlex ID: W2088608529
cites work: Intrinsic regular hypersurfaces in Heisenberg groups
cites work: Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs
cites work: Vanishing viscosity solutions of nonlinear hyperbolic systems
cites work: Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
cites work: Stratified Lie Groups and Potential Theory for their Sub-Laplacians
cites work: An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
cites work: IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES
cites work: Q5848416
cites work: Q4157095
cites work: Continuous solutions for balance laws
cites work: Rectifiability and perimeter in the Heisenberg group
cites work: Regular submanifolds, graphs and area formula in Heisenberg groups
cites work: Q5489518
cites work: Sets with finite \(\mathbb{H}\)-perimeter and controlled normal
DOI: 10.1016/J.JMAA.2009.11.042
description: scientific article; zbMATH DE number 5687660