A sub-Riemannian maximum principle and its application to the p-Laplacian in Carnot groups

DOI10.5186/aasfm.2012.3706zbMath1259.53030OpenAlexW2331667585WikidataQ115159905 ScholiaQ115159905MaRDI QIDQ2908735

Thomas Bieske

Publication date: 5 September 2012

Published in: Annales Academiae Scientiarum Fennicae Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5186/aasfm.2012.3706

zbMATH Keywords

\(p\)-Laplaciansub-Riemannian geometrynon-linear potential theoryvicosity solutions

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Nilpotent and solvable Lie groups (22E25) Other generalizations (nonlinear potential theory, etc.) (31C45) Sub-Riemannian geometry (53C17) Subelliptic equations (35H20) Viscosity solutions to PDEs (35D40)

Related Items (9)

Solving singular evolution problems in sub-Riemannian groups via deterministic games ⋮ Existence and uniqueness of viscosity solutions to the infinity Laplacian relative to a class of Grushin-type vector fields ⋮ On the \(\infty \)-Laplacian on Carnot groups ⋮ A study of comparison, existence and regularity of viscosity and weak solutions for quasilinear equations in the Heisenberg group ⋮ Equivalence of weak and viscosity solutions to the \({\mathtt{p}}(x)\)-Laplacian in Carnot groups ⋮ Characterization by asymptotic mean formulas of \(q\)-harmonic functions in Carnot groups ⋮ Starshapedeness for fully non‐linear equations in Carnot groups ⋮ Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type ⋮ New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs

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