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Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
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Veröffentlicht/Copyright:
25. November 2009
Abstract
We continue to study ℍ-regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group 
endowed with a left-invariant metric d∞ equivalent to its Carnot–Carathéodory metric. Here we investigate their relationships with suitable weak solutions of non-linear first-order PDEs. As a consequence this implies some of their geometric properties: a uniqueness result for ℍ-regular graphs of prescribed horizontal normal as well as their (Euclidean) regularity as long as there is regularity on the horizontal normal.
Keywords.: Heisenberg group; Carnot–Carathéodory metric; intrinsic graph; non-linear first-order PDEs
Received: 2008-12-01
Revised: 2009-05-26
Published Online: 2009-11-25
Published in Print: 2010-March
© de Gruyter 2010
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Artikel in diesem Heft
- Boundary continuity of solutions to a basic problem in the calculus of variations
- Stability for degenerate parabolic equations
- Liouville-type theorems for biharmonic maps between Riemannian manifolds
- Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
- A note on the Wolff potential estimate for solutions to elliptic equations involving measures
Schlagwörter für diesen Artikel
Heisenberg group;
Carnot–Carathéodory metric;
intrinsic graph;
non-linear first-order PDEs
Artikel in diesem Heft
- Boundary continuity of solutions to a basic problem in the calculus of variations
- Stability for degenerate parabolic equations
- Liouville-type theorems for biharmonic maps between Riemannian manifolds
- Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
- A note on the Wolff potential estimate for solutions to elliptic equations involving measures
