Regularity results for quasilinear elliptic equations in the Heisenberg group

DOI10.1007/s00208-007-0121-3zbMath1128.35034OpenAlexW2058357345WikidataQ58880877 ScholiaQ58880877MaRDI QIDQ2458846

Juan J. Manfredi, Giuseppe Mingione

Publication date: 5 November 2007

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-007-0121-3

zbMATH Keywords

regularity of solutionshorizontal gradientsubelliptic nonlinear PDE's

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Subelliptic equations (35H20)

Related Items (50)

\(C^{1,\alpha}\)-regularity for quasilinear degenerate elliptic equation with a drift term on the Heisenberg group ⋮ Partial regularity for discontinuous sub-elliptic systems with VMO-coefficients involving controllable growth terms in Heisenberg groups ⋮ Optimal partial regularity for nonlinear sub-elliptic systems with Dini continuous coefficients in Carnot groups ⋮ Gradient regularity for elliptic equations in the Heisenberg group ⋮ \(L^p\) estimates for weak solutions to nonlinear degenerate parabolic systems ⋮ Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group ⋮ Strict starshapedness of solutions to the horizontal \(p\)-Laplacian in the Heisenberg group ⋮ Regularity of quasi-linear equations with Hörmander vector fields of step two ⋮ \(p\)-harmonic functions in the Heisenberg group: boundary behaviour in domains well-approximated by non-characteristic hyperplanes ⋮ Partial interior regularity for sub-elliptic systems with dini continuous coefficients in Carnot groups: the sub-quadratic controllable case ⋮ Nonlinear elliptic equations on Carnot groups ⋮ Weak differentiability to nonuniform nonlinear degenerate elliptic systems under \(p\), \(q\)-growth condition on the Heisenberg group ⋮ Variational approach to the asymptotic mean-value property for the \(p\)-Laplacian on Carnot groups ⋮ Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group ⋮ Optimal partial regularity for sub-elliptic systems with sub-quadratic growth in Carnot groups ⋮ Regularity for $p$-Harmonic Functions in the Grušin Plane ⋮ Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group ⋮ Some remarks on gradient-type systems on the Heisenberg group ⋮ Interior pointwise gradient estimates for quasilinear elliptic equations in Heisenberg group ⋮ \(\mathrm{HW}^{2, 2}_\mathrm{loc}\)-regularity for \(p\)-harmonic functions in Heisenberg groups ⋮ \(C^{1, \alpha}\)-regularity of quasilinear equations on the Heisenberg group ⋮ Regularity results for a class of obstacle problems in Heisenberg groups. ⋮ Unnamed Item ⋮ Hölder regularity of quasiminimizers to generalized Orlicz functional on the Heisenberg group ⋮ HÖLDER CONTINUITY OF WEAK SOLUTIONS FOR DEGENERATE QUASILINEAR SUBELLIPTIC SYSTEMS WITH DIFFERENT WEIGHTS ⋮ \(C^{1, \alpha}\)-regularity for variational problems in the Heisenberg group ⋮ On the 𝐶^{1,𝛼} regularity of 𝑝-harmonic functions in the Heisenberg group ⋮ On local Lipschitz regularity for quasilinear equations in the Heisenberg group ⋮ 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 ⋮ Conformality and \(Q\)-harmonicity in sub-Riemannian manifolds ⋮ Optimal partial regularity for sub-elliptic systems with Dini continuous coefficients under the superquadratic natural growth ⋮ Optimal partial regularity for weak solutions of nonlinear sub-elliptic systems in Carnot groups ⋮ Maximum principles and nonexistence results for radial solutions to equations involvingp-Laplacian ⋮ Partial regularity for sub-elliptic systems with Dini continuous coefficients involving natural growth terms in the Heisenberg group ⋮ On the Regularity of Nonlinear Subelliptic Equations ⋮ Regularity results for minimizers of \((2,q)\)-growth functionals in the Heisenberg group ⋮ \(C^{1,\alpha }\)-subelliptic regularity on \(\text{SU}(3)\) and compact, semi-simple Lie groups ⋮ Unnamed Item ⋮ Optimal partial regularity for sub-elliptic systems related to Hörmander's vector fields: the controllable growth case ⋮ Mean value property and harmonicity on Carnot-Carathéodory groups ⋮ Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type ⋮ Partial regularity for discontinuous sub-elliptic systems with subquadratic growth in the Heisenberg group ⋮ Nonlinear subelliptic equations ⋮ Partial regularity for nonlinear subelliptic systems with Dini continuous coefficients in Heisenberg groups ⋮ Gradient bounds for the horizontal \(p\)-Laplacian on a Carnot group and some applications ⋮ Green functions for a class of nonlinear degenerate operators with X-ellipticity ⋮ Regularity results for \(p\)-harmonic functions in higher order Grušin planes ⋮ Hölder continuity for nonlinear sub-elliptic systems with sub-quadratic growth

Cites Work

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• Lie groups
• \(C^{1,\alpha}\) local regularity for the solutions of the \(p\)-Laplacian on the Heisenberg group for \(2 \leq p < 1 + \sqrt{5}\)
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