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Uniform domains and quasiconformal map**s on the Heisenberg group
We prove that in the Heisenberg group the image of a uniform domain under a global quasiconformal homeomorphism is still a uniform domain. As a consequence, the class of NTA (non-tangentially accessible) domai...
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Article
Subelliptic mollifiers and a basic pointwise estimate of Poincaré type
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Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for carnot-carathéodory metrics
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Regularity for quasilinear equations and \(1-\) quasiconformal maps in Carnot groups
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Legendrian energy minimizers. Part I: Heisenberg group target
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Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimiz...
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Article
Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces
We study the relationship between the geometry of hypersurfaces in a Carnot-Carathéodory (CC) space and the Ahlfors regularity of the corresponding perimeter measure. To this end we establish comparison theore...
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The mixed problem in L p for some two-dimensional Lipschitz domains
We consider the mixed problem, $$\left\{ \begin{array}{ll} \Delta u = 0 \quad & {\rm in }\, \Omega\\ \frac{\partial u }{\partial \nu} ...
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A subelliptic analogue of Aronson–Serrin’s Harnack inequality
We study the Harnack inequality for weak solutions of a class of degenerate parabolic quasilinear PDE $$\begin{aligned} \partial _t u=...
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Open AccessRegularity for subelliptic PDE through uniform estimates in multi-scale geometries
We aim at reviewing and extending a number of recent results addressing stability of certain geometric and analytic estimates in the Riemannian approximation of subRiemannian structures. In particular we exten...
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Open AccessConformal equivalence of visual metrics in pseudoconvex domains
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains in
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The asymptotic p-Poisson equation as \(p \rightarrow \infty \) in Carnot-Carathéodory spaces
In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as \(p\rightarrow +\infty \) ...
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Article
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 ...