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

DOI10.1016/j.jmaa.2009.11.042zbMath1186.35030OpenAlexW2088608529MaRDI QIDQ961055

Francesco Serra Cassano, Francesco Bigolin

Publication date: 29 March 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.11.042

zbMATH Keywords

Heisenberg groupBurgers' equationCarnot Carathéodory metric

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Analysis on real and complex Lie groups (22E30) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (13)

The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds ⋮ Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ Area formula for regular submanifolds of low codimension in Heisenberg groups ⋮ Intersections of intrinsic submanifolds in the Heisenberg group ⋮ Intrinsic Difference Quotients ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Sets with finite \(\mathbb{H}\)-perimeter and controlled normal ⋮ Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem ⋮ The graphs of Lipschitz functions and minimal surfaces on Carnot groups ⋮ Regularity of minimal intrinsic graphs in 3-dimensional sub-Riemannian structures of step 2 ⋮ Uniqueness of generalized \(p\)-area minimizers and integrability of a horizontal normal in the Heisenberg group ⋮ Lipschitz graphs and currents in Heisenberg groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sets with finite \(\mathbb{H}\)-perimeter and controlled normal
• Intrinsic regular hypersurfaces in Heisenberg groups
• Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Regular submanifolds, graphs and area formula in Heisenberg groups
• Continuous solutions for balance laws
• Vanishing viscosity solutions of nonlinear hyperbolic systems
• Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
• IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Rectifiability and perimeter in the Heisenberg group

This page was built for publication: Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups