Optimal partial regularity for weak solutions of nonlinear sub-elliptic systems in Carnot groups

DOI10.1016/j.na.2010.01.048zbMath1191.35086OpenAlexW2023815924MaRDI QIDQ965028

Jia Lin Wang, Peng Cheng Niu

Publication date: 21 April 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.01.048

zbMATH Keywords

\({\mathcal A}\)-harmonic approximationCaccioppoli type inequalitiessuper-quadratic structure condition

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (16)

Partial regularity for discontinuous sub-elliptic systems with VMO-coefficients involving controllable growth terms in Heisenberg groups ⋮ Partial regularity up to the boundary for solutions of subquadratic elliptic systems ⋮ Optimal partial regularity for nonlinear sub-elliptic systems with Dini continuous coefficients in Carnot groups ⋮ Partial interior regularity for sub-elliptic systems with dini continuous coefficients in Carnot groups: the sub-quadratic controllable case ⋮ Optimal partial regularity for sub-elliptic systems with sub-quadratic growth in Carnot groups ⋮ Some remarks on gradient-type systems on the Heisenberg group ⋮ Optimal partial regularity for nonlinear sub-elliptic systems ⋮ Gradient-type systems on unbounded domains of the Heisenberg group ⋮ Partial Hölder continuity for nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group ⋮ \(C^1\)-partial regularity for sub-elliptic systems with Dini continuous coefficients in Carnot groups ⋮ Optimal partial regularity for sub-elliptic systems with Dini continuous coefficients under the superquadratic natural growth ⋮ Partial regularity for sub-elliptic systems with Dini continuous coefficients involving natural growth terms in the Heisenberg group ⋮ Optimal partial regularity for sub-elliptic systems related to Hörmander's vector fields: the controllable growth case ⋮ Partial regularity for discontinuous sub-elliptic systems with subquadratic growth in the Heisenberg group ⋮ Partial regularity for nonlinear subelliptic systems with Dini continuous coefficients in Heisenberg groups ⋮ Hölder continuity for nonlinear sub-elliptic systems with sub-quadratic growth

Cites Work

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• Schauder estimates for parabolic nondivergence operators of Hörmander type
• Optimal interior partial regularity for nonlinear elliptic systems under the natural growth condition: the method of A-harmonic approximation
• Partial regularity of minimizers of quasiconvex integrals
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• Regularity for quasilinear equations and 1-quasiconformal maps in Carnot groups
• Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
• Optimal interior partial regularity for nonlinear elliptic systems: The method of \(A\)-harmonic approximation
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Regularity for degenerate elliptic problems via \(p\)-harmonic approximation
• Differentiability of solutions for the non-degenerate \(p\)-Laplacian in the Heisenberg group
• The \(p\)-harmonic approximation and the regularity of \(p\)-harmonic maps
• Gradient regularity for elliptic equations in the Heisenberg group
• Regularity results for quasilinear elliptic equations in the Heisenberg group
• Partial regularity results for subelliptic systems in the Heisenberg group
• The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Regularity for quasilinear second‐order subelliptic equations
• An embedding theorem and the harnack inequality for nonlinear subelliptic equations
• Regularity of quasi-linear equations in the Heisenberg group
• 𝐿^{𝑝} estimates for nonvariational hypoelliptic operators with 𝑉𝑀𝑂 coefficients
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• \(C^{1,\alpha}\) local regularity for the solutions of the \(p\)-Laplacian on the Heisenberg group for \(2 \leq p < 1 + \sqrt{5}\)

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