Regularity for subelliptic PDE through uniform estimates in multi-scale geometries

DOI10.1007/s13373-015-0076-8zbMath1357.35092arXiv1504.04762OpenAlexW1959305508WikidataQ59469303 ScholiaQ59469303MaRDI QIDQ300784

Luca Capogna, Giovanna Citti

Publication date: 29 June 2016

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

Full work available at URL: https://arxiv.org/abs/1504.04762

zbMATH Keywords

sub-Riemannian geometryGaussian estimateslifting vector fieldssubelliptic operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) General theory of PDEs and systems of PDEs with constant coefficients (35E20) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Heat kernel (35K08)

Related Items (13)

Riemannian approximation in Carnot groups ⋮ Heat content asymptotics for sub-Riemannian manifolds ⋮ Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group ⋮ Regularity of quasi-linear equations with Hörmander vector fields of step two ⋮ Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group ⋮ Regularity for $p$-Harmonic Functions in the Grušin Plane ⋮ Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group ⋮ \(C^{1, \alpha}\)-regularity of quasilinear equations on the Heisenberg group ⋮ \(C^{1, \alpha}\)-regularity for variational problems in the Heisenberg group ⋮ Regularity of mean curvature flow of graphs on Lie groups free up to step 2 ⋮ \(C^{1,\alpha }\)-subelliptic regularity on \(\text{SU}(3)\) and compact, semi-simple Lie groups ⋮ Left-invariant geometries on \(\operatorname{SU}(2)\) are uniformly doubling ⋮ Schauder estimates at the boundary for sub-Laplacians in Carnot groups

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