ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP

By Thomas Bieske. 2002

80 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/80336faa12b3a3a3ce46f0176eccc2fd76e9e279

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Regularity of convex functions on Heisenberg groups (2003, methodology): “Using results about viscosity solutions of the subelliptic ∞-Laplacian by Bieske ([5]), they proved that v-convex functions on the Heisenberg group are locally Lipschitz continuous.”
Viscosity convex functions on carnot groups (2003, background): “Proof of Corollary B . It is clear that (b) and (c) are equivalent (see, e.g., [DGN][LMS]).”
A Visit with the ∞-Laplace Equation (2008, methodology): “For papers which treat various geometrical structures, we mention the the work Bieske [15], which was the first, as well as [16], [17], [18] and Wang [51].”
Maximum and Comparison Principles for Convex Functions on the Heisenberg Group (2003, background): “On the Heisenberg group, and more generally in Carnot groups, several notions of convexity have been introduced and compared in Danielli et al. (2003) (horizontal convexity) and Lu et al. (2003) (viscosity convexity).”
Convex functions on the Heisenberg group (2003, background): “Given B H r and B H two concentric balls with respect to the smooth Heisenberg”
The Aronsson equation for absolute minimizers of ${L^\infty}$-functionals associated with vector fields satisfying Hörmander's condition (2003, methodology): “Bieske [B1, B2] proved the uniqueness of viscosity solutions to the subelliptic ∞ -Laplacian equation on the Heisenberg group H n and the Grushin-type space.”
A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS (2004, background): “In the special case of a sub-Riemannian setting, absolute minimizers and the associated generalized infinity Laplace equations have been considered in [19], [20], [21], [22] and [62].”
Polar coordinates in Carnot groups (2002, background): “In fact, non-smooth solutions to (2.6) are usually considered in the viscosity sense; see [8, 28, 33, 9 ]. For C 2 functions f , we can write”
Convex functions on Carnot groups. (2007, background): “1 in [13] was Bieske’s extension to the Heisenberg group of Jensen’s uniqueness theorem for ∞-harmonic functions ([12], [3].”