Quasiconformal mappings with Sobolev boundary values

Kari Astala; Mario Bonk; Juha Heinonen

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 3, page 687-731
  • ISSN: 0391-173X

Abstract

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We consider quasiconformal mappings in the upper half space ℝ + n + 1 of ℝ n + 1 , n ≥ 2 , whose almost everywhere defined trace in ℝ n has distributional differential in L n ( ℝ n ) . We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space H 1 . More generally, we consider certain positive functions defined on ℝ + n + 1 , called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them. The abstract approach of general conformal densities sheds new light to the mapping case as well.

How to cite

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Astala, Kari, Bonk, Mario, and Heinonen, Juha. "Quasiconformal mappings with Sobolev boundary values." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.3 (2002): 687-731. <http://eudml.org/doc/84484>.

@article{Astala2002,
abstract = {We consider quasiconformal mappings in the upper half space $\mathbb \{R\}^\{n+1\}_+$ of $\mathbb \{R\}^\{n+1\}$, $n\ge 2$, whose almost everywhere defined trace in $\mathbb \{R\}^n$ has distributional differential in $L^n(\mathbb \{R\}^n)$. We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space $H^1$. More generally, we consider certain positive functions defined on $\mathbb \{R\}^\{n+1\}_+$, called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them. The abstract approach of general conformal densities sheds new light to the mapping case as well.},
author = {Astala, Kari, Bonk, Mario, Heinonen, Juha},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {687-731},
publisher = {Scuola normale superiore},
title = {Quasiconformal mappings with Sobolev boundary values},
url = {http://eudml.org/doc/84484},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Astala, Kari
AU - Bonk, Mario
AU - Heinonen, Juha
TI - Quasiconformal mappings with Sobolev boundary values
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 3
SP - 687
EP - 731
AB - We consider quasiconformal mappings in the upper half space $\mathbb {R}^{n+1}_+$ of $\mathbb {R}^{n+1}$, $n\ge 2$, whose almost everywhere defined trace in $\mathbb {R}^n$ has distributional differential in $L^n(\mathbb {R}^n)$. We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space $H^1$. More generally, we consider certain positive functions defined on $\mathbb {R}^{n+1}_+$, called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them. The abstract approach of general conformal densities sheds new light to the mapping case as well.
LA - eng
UR - http://eudml.org/doc/84484
ER -

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