Subelliptic p -harmonic maps into spheres and the ghost of Hardy spaces

Hajłasz, Piotr; Strzelecki, Paweł

doi:10.1007/s002080050225

Cited by 32 publications

(32 citation statements)

References 60 publications

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“…Therefore we have This theorem is a generalization of theorems in Barletta and Dragomir (2004) and Hajlasz and Strzelecki (1998).…”

Section: Introduction Main Resultsmentioning

confidence: 80%

“…E. Barletta and S. Dragomir also take use of H-S dual inequality to prove that weakly subelliptic F-harmonic maps into spheres are regular, if F has Q−2 2 -power growth (see Barletta & Dragomir, 2004), and hence generalize the Hajłasz-Strzelecki's regularity. In this paper, we improve the dual inequality of Hajłasz- Strzelecki (1998), and apply it to obtain a regularity lemma of weak solutions of a subelliptic PDE of divergent type. As an application, we get a regularity of weakly subelliptic F-harmonic maps into Riemannian manifolds with transitive isometric transformation groups.…”

Section: Introduction Main Resultsmentioning

confidence: 99%

“…The following subelliptic Sobolev inequality can be found in many papers (see for example Hajlasz & Strzelecki, 1998):…”

Section: Subelliptic Sobolev Inequality and Poincare Inequalitymentioning

confidence: 99%

“…The subelliptic Sobolev inequality implies the following Poincare inequality (see Hajlasz & Strzelecki, 1998;Jerison, 1986):…”

Section: Subelliptic Sobolev Inequality and Poincare Inequalitymentioning

confidence: 99%

“…For a regularity of such a map u, the following dual inequality is established in (Hajlasz & Strzelecki, 1998): …”

Section: Dual Inequality Of Hajlasz-strzelecki Typementioning

confidence: 99%

See 4 more Smart Citations

Regularity of Weakly Subelliptic F-Harmonic Maps

Zhou

2013

JMR

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Let Ω ⊆ R m be a bounded domain, X = {X 1 , X 2 , · · · , X k 0 } be a Hömander family of vector fields on Ω whose homogeneous dimension is Q. In this paper, we improve the dual inequality obtained by P. Hajlasz and P. Strzelecki in 1998, and take use of it to discuss regularity of weakly subelliptic F-harmonic maps into Riemannian manifolds with transitive isometric transformation groups.

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“…Therefore we have This theorem is a generalization of theorems in Barletta and Dragomir (2004) and Hajlasz and Strzelecki (1998).…”

Section: Introduction Main Resultsmentioning

confidence: 80%

Section: Introduction Main Resultsmentioning

confidence: 99%

“…The following subelliptic Sobolev inequality can be found in many papers (see for example Hajlasz & Strzelecki, 1998):…”

Section: Subelliptic Sobolev Inequality and Poincare Inequalitymentioning

confidence: 99%

“…The subelliptic Sobolev inequality implies the following Poincare inequality (see Hajlasz & Strzelecki, 1998;Jerison, 1986):…”

Section: Subelliptic Sobolev Inequality and Poincare Inequalitymentioning

confidence: 99%

“…For a regularity of such a map u, the following dual inequality is established in (Hajlasz & Strzelecki, 1998): …”

Section: Dual Inequality Of Hajlasz-strzelecki Typementioning

confidence: 99%

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Regularity of Weakly Subelliptic F-Harmonic Maps

Zhou

2013

JMR

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Sobolev Mappings between Manifolds and Metric Spaces

Hajłasz

Sobolev Spaces in Mathematics I

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In connection with the theory of p-harmonic mappings, Eells and Lemaire raised a question about density of smooth mappings in the space of Sobolev mappings between manifolds. Recently Hang and Lin provided a complete solution to this problem. The theory of Sobolev mappings between manifolds has been extended to the case of Sobolev mappings with values into metric spaces. Finally analysis on metric spaces, the theory of CarnotCarathéodory spaces, and the theory of quasiconformal mappings between metric spaces led to the theory of Sobolev mappings between metric spaces. The purpose of this paper is to provide a self-contained introduction to the theory of Sobolev spaces between manifolds and metric spaces.

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Geometry of Carnot-Carathéodory Spaces, Differentiability, Coarea and Area Formulas

Карманова

Vodop’yanov

2009

Analysis and Mathematical Physics

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We give a simple proof of Gromov's Theorem on nilpotentization of vector fields, and exhibit a new method for obtaining quantitative estimates of comparing geometries of two different local Carnot groups in Carnot-Carathéodory spaces with C 1,α -smooth basis vector fields, α ∈ [0, 1]. From here we obtain the similar estimates for comparing geometries of a Carnot-Carathéodory space and a local Carnot group. These two theorems imply basic results of the theory: Gromov type Local Approximation Theorems, and for α > 0 Rashevskiǐ-Chow Theorem and Ball-Box Theorem, etc. We apply the obtained results for proving hc-differentiability of mappings of Carnot-Carathéodory spaces with continuous horizontal derivatives. The latter is used in proving the coarea formula for some classes of contact mappings of Carnot-Carathéodory spaces.

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Subelliptic p -harmonic maps into spheres and the ghost of Hardy spaces

Cited by 32 publications

References 60 publications

Regularity of Weakly Subelliptic F-Harmonic Maps

Regularity of Weakly Subelliptic F-Harmonic Maps

Sobolev Mappings between Manifolds and Metric Spaces

Geometry of Carnot-Carathéodory Spaces, Differentiability, Coarea and Area Formulas

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