Communications in Contemporary MathematicsAccepted Papers No AccessContinuous primitives for higher degree differential forms euclidean spaces, heisenberg groups and applicationsAnnalisa Baldi, Bruno Franchi, Pierre PansuAnnalisa Franchi Search more papers by this author , Pansu https://doi.org/10.1142/S0219199725500233Cited by:0 (Source: Crossref) PreviousNext AboutFiguresReferencesRelatedDetailsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend Library ShareShare...

Let $1<p<\infty$. In this article we establish an $L^p$-Hodge decomposition theorem on sub-Riemannian compact contact manifolds without boundary, related to the Rumin complex of differential forms. Given $L^p$- Rumin's form, adopt approach in spirit Morrey's book obtain a with higher regular ``primitives'' i.e. that belong suitable Sobolev classes. Our proof relies recent results obtained [4] and [6].

Abstract On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using Rumin complex has been considered in (M. Rumin, “Differential geometry C-C spaces and application to Novikov-Shubin numbers nilpotent Lie groups,” C. R. Acad. Sci., Paris Sér. I Math. , vol. 329, no. 11, pp. 985–990, 1999, M. “Sub-Riemannian limit differential form spectrum contact manifolds,” Geom. Funct. Anal. 10, 2, 407–452, 2000), where author introduced 0-order pseudodifferential...

It is shown that higher degree exact differential forms on compact Riemannian $n$-manifolds possess continuous primitives whose uniform norm controlled by their $L^n$ norm. A contact sub-Riemannian analogue proven, with replaced Rumin forms.

Let \mathcal L be a non-negative self-adjoint N\times N matrix-valued operator of order a\leq Q on Carnot group \mathbb G . Here is the homogeneous dimension The aim this paper to investigate relationship between hypoellipticity and maximal (i.e. sharp L^p estimates in appropriate Sobolev spaces), -maximal spaces for { 1 &lt; p \infty }), what we call subellipticity (which basically higher energy estimate).

In this paper we prove a compensated compactness theorem for differential forms in the contact complex of Heisenberg group. The proof relies on L p -Hodge decomposition intrinsic forms, and suitable estimates Laplace operator associated with complex.

This paper addresses one of the new and most important issues arising when low-power voltage transformers (LPVTs) are used in power network substations for evaluating, among others, residual measurement. Conversely to open-triangle inductive instrument transformers, use phase measuring gets challenging due very high accuracy required three LPVTs. In this paper, a general expression estimate measurement uncertainty, starting from LPVTs accuracy, is presented. The effectiveness proposed...

Abstract In this paper, we prove contact Poincaré and Sobolev inequalities in Heisenberg groups $\mathbb{H}^{n}$ , where the word ‘contact’ is meant to stress that de Rham’s exterior differential replaced by of so-called Rumin complex $(E_{0}^{\bullet },d_{c})$ which recovers scale invariance under group dilations associated with stratification Lie algebra . addition, construct smoothing operators for forms on sub-Riemannian manifolds bounded geometry, act trivially cohomology. For instance,...

Abstract Let G be a free Carnot group (i.e. connected simply nilpotent stratified Lie group) of step 2. In this paper, we prove that the variational functional generated by “intrinsic” Maxwell’s equations in is Γ-limit sequence classical Euclidean) functionals associated with strongly anisotropic dielectric permittivity and magnetic permeability Euclidean space.

In this paper we study Mumford–Shah-type functionals associated with doubling metric measures or strong A ∞ weights in the setting of perimeter theory sense Ambrosio and Miranda spaces. We prove an existence theorem a suitably defined class special BV functions.