Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Quasilinear parabolic equations with (p)-Laplacian (35K92)

Cites Work

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Regularity for subelliptic PDE through uniform estimates in multi-scale geometries
Degenerate parabolic equations
Everywhere-regularity for some quasilinear systems with a lack of ellipticity
An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
Harnack estimates for quasi-linear degenerate parabolic differential equations
Singular solutions of the \(p\)-Laplace equation
Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
Regularity for a more general class of quasilinear equations
Regularity for a class of nonlinear elliptic systems
Regularity for quasilinear equations and 1-quasiconformal maps in Carnot groups
Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature
Conformality and \(Q\)-harmonicity in sub-Riemannian manifolds
The Poincaré inequality for vector fields satisfying Hörmander's condition
A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
Differentiability of solutions for the non-degenerate \(p\)-Laplacian in the Heisenberg group
On local Lipschitz regularity for quasilinear equations in the Heisenberg group
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
\(C^{1, \alpha}\)-regularity for variational problems in the Heisenberg group
\(C^{1,\alpha }\)-subelliptic regularity on \(\text{SU}(3)\) and compact, semi-simple Lie groups
Hölder gradient estimates for parabolic homogeneous \(p\)-Laplacian equations
Gradient regularity for elliptic equations in the Heisenberg group
Local behavior of solutions of quasi-linear equations
Harnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-Laplacian
Regularity results for quasilinear elliptic equations in the Heisenberg group
Hypoelliptic second order differential equations
Isolated singularities of solutions of quasi-linear equations
A tour of subriemannian geometries, their geodesics and applications
Functional Analysis, Calculus of Variations and Optimal Control
Subelliptic Cordes estimates
Continuity of Solutions of Parabolic and Elliptic Equations
C1 + α local regularity of weak solutions of degenerate elliptic equations
p-Harmonic Functions in the Plane
Hälder regularity for the gradient of solutions of certain singular parabolic systems
Regularity for quasilinear second‐order subelliptic equations
Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
Regularity of quasi-linear equations in the Heisenberg group
Sobolev met Poincaré
On the 𝐶^{1,𝛼} regularity of 𝑝-harmonic functions in the Heisenberg group
The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
Riemannian approximation in Carnot groups
A harnack inequality for parabolic differential equations
Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations

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