Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs

DOI10.1515/ACV.2010.004zbMath1188.53027MaRDI QIDQ3400074

Francesco Bigolin, Francesco Serra Cassano

Publication date: 5 February 2010

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

zbMATH Keywords

Heisenberg groupintrinsic graphCarnot-Caratheodory metricnonlinear first-order PDEs

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Sub-Riemannian geometry (53C17)

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Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux. I., Some remarks about parametrizations of intrinsic regular surfaces in the Heisenberg group, 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, Intrinsic Lipschitz graphs in Carnot groups of step 2, Intrinsic Difference Quotients, Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group, Intrinsic differentiability and intrinsic regular surfaces in Carnot groups, Sets with finite \(\mathbb{H}\)-perimeter and controlled normal, Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem, Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\), Regularity estimates for continuous solutions of \(\alpha\)-convex balance laws, Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups, Blow-up estimates at horizontal points and applications, Regularity of minimal intrinsic graphs in 3-dimensional sub-Riemannian structures of step 2, Intrinsic regular surfaces of low codimension in Heisenberg groups, Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity, Boundedness of singular integrals on \(C^{1,{\alpha}}\) intrinsic graphs in the Heisenberg group, Lipschitz graphs and currents in Heisenberg groups

Cites Work

• \(H\)-minimal graphs of low regularity in \(\mathbb H^1\)
• The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
• A notion of rectifiability modeled on Carnot groups
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Rectifiability and perimeter in the Heisenberg group