The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carathéodory metrics

DOI10.1090/S0002-9947-04-03601-3zbMath1058.35067OpenAlexW1757010007MaRDI QIDQ4825673

Luca Capogna, Thomas Bieske

Publication date: 28 October 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03601-3

zbMATH Keywords

sub-Riemannian geometryabsolute minimizersinfinite sub-Laplacian

Mathematics Subject Classification ID

Sub-Riemannian geometry (53C17) Subelliptic equations (35H20)

Related Items

The Dirichlet problem for fully nonlinear elliptic equations non-degenerate in a fixed direction, A tour of the theory of absolutely minimizing functions, Solving singular evolution problems in sub-Riemannian groups via deterministic games, The Aronsson equation for absolute minimizers of supremal functionals in Carnot–Carathéodory spaces, On the \(\infty \)-Laplacian on Carnot groups, \(L^{\infty }\) variational problems for maps and the Aronsson PDE system, Geometric second derivative estimates in Carnot groups and convexity, Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian, Lipschitz extensions on generalized Grushin spaces, Aronsson's equations on Carnot-Carathéodory spaces, New properties of convex functions in the Heisenberg group, Starshapedeness for fully non‐linear equations in Carnot groups, The Aronsson equation, Lyapunov functions, and local Lipschitz regularity of the minimum time function, Properties of infinite harmonic functions on Grushin-type spaces, New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs, The 𝑃-Laplace equation on a class of Grushin-type spaces, The Aronsson equation for absolute minimizers of $\{L^\infty \}$-functionals associated with vector fields satisfying Hörmander’s condition, Role of fundamental solutions for optimal Lipschitz extensions on hyperbolic space

Cites Work

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• Lipschitz extensions on generalized Grushin spaces
• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• On Carnot-Caratheodory metrics
• Balls and metrics defined by vector fields. I: Basic properties
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• Differentiability of Lipschitz functions on metric measure spaces
• An efficient derivation of the Aronsson equation
• Convex functions on the Heisenberg group
• Lectures on analysis on metric spaces
• Viscosity solutions on Grushin-type planes
• Sobolev spaces on an arbitrary metric space
• Notion of convexity in Carnot groups
• Hypoelliptic second order differential equations
• Extension of functions satisfying Lipschitz conditions
• On the partial differential equation \(u_ x^ 2 u_{xx} +2u_ x u_ y u_{xy} +u_ y^ 2 u_{yy} = 0\)
• On the best possible character of the 𝐿^{𝑄} norm in some a priori estimates for non-divergence form equations in Carnot groups
• ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• Partial differential equations
• The Euler equation and absolute minimizers of \(L^\infty\) functionals
• Optimal Lipschitz extensions and the infinity Laplacian