Results 81 to 90 of about 2,092 (183)

Morrey–Campanato functional spaces for Carnot groups

Banach Journal of Mathematical Analysis
Abstract We shortly review the historical path of Morrey–Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey–Campanato spaces in the framework of Carnot groups.
Nicolò Cangiotti, Marco Capolli
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Chaotic Geodesics in Carnot Groups

, 1997
The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corresponds to the superdiagonal. We prove that the associated subRiemannian geodesic flow is not completely integrable.
Montgomery, R., Shapiro, M., Stolin, A.
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Morrey estimates for subelliptic p-Laplace type systems with VMO coefficients in Carnot groups

Electronic Journal of Differential Equations, 2016
In this article, we study estimates in Morrey spaces to the horizontal gradient of weak solutions for a class of quasilinear sub-elliptic systems of p-Laplace type with VMO coefficients under the controllable growth over Carnot group if p is not too
Haiyan Yu, Shenzhou Zheng
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Lipschitz and bilipschitz maps on Carnot groups [PDF]

Pacific Journal of Mathematics, 2013
Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of A of positive Hausdorff measure.
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Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups

Bruno Pini Mathematical Analysis Seminar, 2010
Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S.
Francesco Paolo Montefalcone
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Optimizing a machine learning design of dielectric properties in lead-free piezoelectric ceramics

Materials & Design
Designing lead-free piezoelectric ceramics with tailored electrical properties remains a critical challenge for various applications. In this paper we present a novel methodology integrating Machine Learning (ML) and optimization procedures to fine-tune ...
Helder R.O. Rocha, Roy Roukos, Sara Abou Dargham, Jimmy Romanos, Denis Chaumont, Jair A.L. Silva, Heinrich Wörtche   +6 more
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Performance of plant-produced RBDs as SARS-CoV-2 diagnostic reagents: a tale of two plant platforms

Frontiers in Plant Science
The COVID-19 pandemic has underscored the need for rapid and cost-effective diagnostic tools. Serological tests, particularly those measuring antibodies targeting the receptor-binding domain (RBD) of the virus, play a pivotal role in tracking infection ...
Mattia Santoni, Noemi Gutierrez-Valdes, Denise Pivotto, Elena Zanichelli, Anthony Rosa, Guillermo Sobrino-Mengual, Guillermo Sobrino-Mengual, Juliette Balieu, Patrice Lerouge, Muriel Bardor, Riccardo Cecchetto, Monica Compri, Annarita Mazzariol, Anneli Ritala, Linda Avesani   +14 more
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The p-Laplace equation in a class of Hormander vector fields

Electronic Journal of Differential Equations, 2019
We find the fundamental solution to the p-Laplace equation in a class of Hormander vector fields that generate neither a Carnot group nor a Grushin-type space. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding
Thomas Bieske, Robert D. Freeman
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Isodiametric inequality in Carnot groups

Annales Academiae Scientiarum Fennicae Mathematica, 2011
The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups. We prove that for any Carnot group equipped with a Haar measure one can find a homogeneous distance for which this fails to hold. We also consider Carnot-Caratheodory
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Coercive inequalities on Carnot groups: taming singularities

Analysis and Mathematical Physics
AbstractIn the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. To this end, we develop a technique to introduce natural singularities in the energy function U in order to force one of the coercivity conditions.
Bou Dagher, E., Zegarliński, B.
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