Role of fundamental solutions for optimal Lipschitz extensions on hyperbolic space

DOI10.1016/j.jde.2005.07.004zbMath1084.35019OpenAlexW1981402677MaRDI QIDQ2576182

Imran H. Biswas, Adimurthi

Publication date: 8 December 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2005.07.004

zbMATH Keywords

viscosity solutionfundamental solutionhyperbolic space\(p\)-Laplace-Beltrami operatorinfinity Laplace-Beltrami operatoroptimal Lipschitz extension

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Nonlinear elliptic equations (35J60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Cites Work

• \(C^1\) regularity for infinity harmonic functions in two dimensions
• Lipschitz extensions on generalized Grushin spaces
• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• Viscosity solutions on Grushin-type planes
• 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 ∞-HARMONIC FUNCTIONS ON THE HEISENBERG GROUP
• A tour of the theory of absolutely minimizing functions
• The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carathéodory metrics
• Optimal Lipschitz extensions and the infinity Laplacian
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