On the \(\infty \)-Laplacian on Carnot groups

DOI10.1007/s10958-022-06198-9OpenAlexW4309885835MaRDI QIDQ2683652

Juan J. Manfredi, Nicolò Forcillo, Fausto Ferrari

Publication date: 14 February 2023

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-022-06198-9

zbMATH Keywords

Lipschitz estimates\(\infty \)-Laplacian on Carnot groups

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Cites Work

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• Properties of infinite harmonic functions on Grushin-type spaces
• Superposition principle on the viscosity solutions of infinity Laplace equations
• Inhomogeneous infinity Laplace equation
• A sub-Riemannian maximum principle and its application to the p-Laplacian in Carnot groups
• The Aronsson equation for absolute minimizers of $\{L^\infty \}$-functionals associated with vector fields satisfying Hörmander’s condition
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• 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
• Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds
• Surface measures in Carnot-Carathéodory spaces

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