Subelliptic harmonic maps
TL;DR: In this paper, a nonlinear harmonic map type system of subelliptic PDE was studied and the Dirichlet problem with image contained in a convex ball was solved.
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Abstract: We study a nonlinear harmonic map type system of subelliptic PDE In particular, we solve the Dirichlet problem with image contained in a convex ball
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Citations
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Sobolev met Poincaré
Piotr Hajłasz,Pekka Koskela +1 more
- 01 Jan 2000
TL;DR: In this article, the Poincare and Sobolev inequalities, pointwise estimates, and pointwise classifications of Soboleve classes are discussed. But they do not cover the necessary conditions for Poincarse inequalities.
Generalized Dirichlet forms and harmonic maps
TL;DR: In this article, a nonlinear version of Dirichlet spaces is developed for generalized harmonic maps with values in metric spaces instead of scalar functions, and the Holder continuity of minimizers is shown if a ball doubling property and a Poincare inequality hold.
136
Geometry of Carnot-Caratheodory Spaces, Differentiability, Coarea and Area Formulas
Maria Karmanova,Sergey Vodop′yanov +1 more
- 01 Jan 2009
TL;DR: In this paper, the authors compare geometries of two different local Lie groups in a Carnot-Caratheodory space, and obtain quantitative estimates of their difference, based on Gromov's Theorem on nilpotentization of vector fields for which they give new and simple proof.
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Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces
Piotr Hajłasz,Paweł Strzelecki +1 more
TL;DR: Coifman, Lions, Meyer and Semmes as mentioned in this paper showed that a nonnegative function belongs to the Hardy space if and only if it belongs locally to L log L. The result is quite intriguing, since a priori Holder inequality implies only that Ju ∈ L1 and one does not suspect any higher integrability.
References
Hypoelliptic second order differential equations
TL;DR: In this paper, it was shown that the sufficient conditions for hypoelliptie are not satisfied by the equation, and that the necessary conditions are not sufficient for all differential equations with constant coefficients.
Hypoelliptic differential operators and nilpotent groups
TL;DR: In this paper, the authors present sufficient condi t ions for hypoe l l l ip t i c i ty... this paper..,.. The authors present a free Lie-A-Lgebras analysis on the p roof of the T h eo rem.