Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group
This note provides a succinct survey of the existing literature concerning the Hölder
regularity for the gradient of weak solutions of PDEs of the form∑ i= 1 2 n X i A i (∇ 0 u)= 0 …
regularity for the gradient of weak solutions of PDEs of the form∑ i= 1 2 n X i A i (∇ 0 u)= 0 …
Regularity of quasi-linear equations with Hörmander vector fields of step two
If the smooth vector fields X 1,…, X m and their commutators span the tangent space at every
point in Ω⊆ RN for any fixed m≤ N, then we establish the full interior regularity theory of …
point in Ω⊆ RN for any fixed m≤ N, then we establish the full interior regularity theory of …
1,-regularity for variational problems in the Heisenberg group
S Mukherjee, X Zhong - Anal. PDE, 2021 - msp.org
Following [Zhong 2017], we continue to study in this paper the regularity of minima of scalar
variational integrals in the Heisenberg group n, n 1. Let be a domain in n and u W! a …
variational integrals in the Heisenberg group n, n 1. Let be a domain in n and u W! a …
Random walks and random tug of war in the Heisenberg group
We study mean value properties of p p-harmonic functions on the first Heisenberg group HH,
in connection to the dynamic programming principles of certain stochastic processes. We …
in connection to the dynamic programming principles of certain stochastic processes. We …
-subelliptic regularity on and compact, semi-simple Lie groups
A Domokos, JJ Manfredi - Analysis and Mathematical Physics, 2020 - Springer
Let the vector fields X_1, ..., X_ 6 X 1,…, X 6 form an orthonormal basis of HH, the orthogonal
complement of a Cartan subalgebra (of dimension 2) in\, SU\,(3) SU (3). We prove that weak …
complement of a Cartan subalgebra (of dimension 2) in\, SU\,(3) SU (3). We prove that weak …
On the 𝐶^{1, 𝛼} regularity of 𝑝-harmonic functions in the Heisenberg group
D Ricciotti - Proceedings of the American Mathematical Society, 2018 - ams.org
On the 𝐶^{1,𝛼} regularity of 𝑝-harmonic functions in the Heisenberg group Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 146, Number 7 …
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 146, Number 7 …
Lipschitz regularity for solutions of the parabolic -Laplacian in the Heisenberg group
We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic
PDEs modeled on the parabolic $ p $-Laplacian $$\p_t u=\sum_ {i= 1}^{2n} X_i (|\nabla_0 …
PDEs modeled on the parabolic $ p $-Laplacian $$\p_t u=\sum_ {i= 1}^{2n} X_i (|\nabla_0 …
Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group
We extend to the parabolic setting some of the ideas originated with **ao Zhong's proof
in\cite {Zhong} of the H\" older regularity of $ p-$ harmonic functions in the Heisenberg group …
in\cite {Zhong} of the H\" older regularity of $ p-$ harmonic functions in the Heisenberg group …
p-harmonic coordinates for H\" older metrics and applications
We show that on any Riemannian manifold with H\" older continuous metric tensor, there
exists a $ p $-harmonic coordinate system near any point. When $ p= n $ this leads to a …
exists a $ p $-harmonic coordinate system near any point. When $ p= n $ this leads to a …
Riemannian approximation in Carnot groups
A Domokos, JJ Manfredi, D Ricciotti - Proceedings of the Royal …, 2022 - cambridge.org
We present self-contained proofs of the stability of the constants in the volume doubling
property and the Poincaré and Sobolev inequalities for Riemannian approximations in …
property and the Poincaré and Sobolev inequalities for Riemannian approximations in …