Lipschitz extensions on generalized Grushin spaces

DOI10.1307/mmj/1114021082zbMath1086.35023OpenAlexW2087528922MaRDI QIDQ558692

Thomas Bieske

Publication date: 13 July 2005

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1114021082

zbMATH Keywords

viscosity solutionminimizercomparison principlesGrushin space

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Graded Lie (super)algebras (17B70) Subelliptic equations (35H20)

Related Items

A tour of the theory of absolutely minimizing functions ⋮ The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carathéodory metrics ⋮ Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields ⋮ Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds ⋮ Aronsson's equations on Carnot-Carathéodory spaces ⋮ The \(\infty \)-capacity and Faber-Krahn inequality on Grushin spaces ⋮ Properties of infinite harmonic functions on Grushin-type spaces ⋮ The Carnot-Carathéodory distance and the infinite Laplacian ⋮ 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

• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Partial differential equations. 4th ed
• Hypoelliptic differential operators and nilpotent groups
• An efficient derivation of the Aronsson equation
• Double sequence core theorems
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• User’s guide to viscosity solutions of second order partial differential equations
• ON ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carathéodory metrics
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