Results 51 to 60 of about 18,321 (180)
APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS [PDF]
Communications in Contemporary Mathematics, 2011 This paper deals with a notion of Sobolev space W1, pintroduced by Bourgain, Brezis and Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by Ponce to obtain a Poincaré-type inequality.
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On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups
, 2016 We show by explicit estimates that the SubRiemannian distance in a Carnot group of step two is locally semiconcave away from the diagonal if and only if the group does not contain abnormal minimizing curves.
Montanari, Annamaria +1 more
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Nonlinear Pulse Shaping in Fibres for Pulse Generation and Optical Processing
International Journal of Optics, 2012 The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science.
Sonia Boscolo, Christophe Finot
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Almost uniform domains and Poincaré inequalities
Transactions of the London Mathematical Society, 2021 Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure.
Sylvester Eriksson‐Bique, Jasun Gong
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A proof of Hörmander’s theorem for sublaplacians on Carnot groups [PDF]
Nonlinear Analysis, 2015 Let \(G\) be a Carnot group and let \(\mathcal{L}\) be its left-invariant sub-Laplacian. As a consequence of Hörmander's theorem, \(\mathcal{L}\) is hypoelliptic, that is, for every distribution \(u\) on \(G\), if \(\mathcal{L}u \in C^\infty\), then \(u \in C^\infty\).
Bramanti, Marco, Brandolini, Luca
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W2,p a priori estimates for nonvariational operators: the sharp maximal function technique
Bruno Pini Mathematical Analysis Seminar, 2018 We consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hörmander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the ...
Marco Bramanti
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Rankine Carnot Batteries with the Integration of Thermal Energy Sources: A Review
Energies, 2020 This paper provides an overview of a novel electric energy storage technology. The Thermally Integrated Pumped Thermal Electricity Storage (TI-PTES) stores electric energy as thermal exergy.
Guido Francesco Frate +2 more
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Metric currents, differentiable structures, and Carnot groups [PDF]
, 2011 We examine the theory of metric currents of Ambrosio and Kirchheim in the setting of spaces admitting differentiable structures in the sense of Cheeger and Keith.
Williams, Marshall
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Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results
, 2018 In this paper we attempt to give a systematic account on privileged coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold with a distinguished filtration of subbundles of the tangent bundle which is ...
Choi, Woocheol, Ponge, Raphael
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The Isoperimetric Problem in Carnot-Caratéodory Spaces
Bruno Pini Mathematical Analysis Seminar, 2017 We present some recent results obtained on the isoperimetric problem in a class of Carnot-Carathéodory spaces, related to the Heisenberg group. This is the framework of Pansu’s conjecture about the shape of isoperimetric sets.
Valentina Franceschi
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