17 Result(s)

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 ...

Luca Capogna, Giovanna Citti, **ao Zhong in Vietnam Journal of Mathematics (2024)

Article

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 \(p\rightarrow +\infty \) ...

Luca Capogna, Gianmarco Giovannardi, Andrea Pinamonti… in Mathematische Annalen (2024)

Chapter and Conference Paper

Robust Neural Network Approach to System Identification in the High-Noise Regime

We present a new algorithm for learning unknown governing equations from trajectory data, using a family of neural networks. Given samples of solutions x(t) to an unknown dynamical system

Elisa Negrini, Giovanna Citti, Luca Capogna in Learning and Intelligent Optimization (2023)

Chapter

L ^∞-Extremal Map**s in AMLE and Teichmüller Theory

These lecture focus on two vector-valued extremal problems which have a common feature in that the corresponding energy functionals involve L ^∞ norm of ...

Luca Capogna in Fully Nonlinear PDEs in Real and Complex Geometry and Optics (2014)

Article

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=...

Luca Capogna, Giovanna Citti, Garrett Rea in Mathematische Annalen (2013)

Article

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} ...

Loredana Lanzani, Luca Capogna, Russell M. Brown in Mathematische Annalen (2008)

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...

Luca Capogna, Nicola Garofalo in The Journal of Geometric Analysis (2006)

Article

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...

Luca Capogna, Nicola Garofalo in Journal of the European Mathematical Society (2003)

Article

Legendrian energy minimizers. Part I: Heisenberg group target

Luca Capogna, Fang-Hua Lin in Calculus of Variations and Partial Differential Equations (2001)

Article

Regularity for quasilinear equations and \(1-\) quasiconformal maps in Carnot groups

Luca Capogna in Mathematische Annalen (1999)

Article

Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for carnot-carathéodory metrics

Luca Capogna, Nicola Garofalo in Journal of Fourier Analysis and Applications (1998)

Article

Subelliptic mollifiers and a basic pointwise estimate of Poincaré type

Luca Capogna, Donatella Danielli, Nicola Garofalo in Mathematische Zeitschrift (1997)

Article

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...

Luca Capogna, Puqi Tang in manuscripta mathematica (1995)