Limits of Sobolev homeomorphisms

Tadeusz Iwaniec; Jani Onninen

doi:10.4171/JEMS/671

Limits of Sobolev homeomorphisms

Tadeusz Iwaniec, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Let X,Y R² be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X onto → Y in the Sobolev space W ^1,p(X,R²), p ≥ 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.

Original language	English (US)
Pages (from-to)	473-505
Number of pages	33
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/671
State	Published - 2017

Keywords

Approximation of Sobolev homeomorphisms
Energy-minimal deformations
Harmonic mappings
P-harmonic equation
Variational integrals

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/JEMS/671

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abstract = "Let X,Y R2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X onto → Y in the Sobolev space W 1,p(X,R2), p ≥ 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.",

keywords = "Approximation of Sobolev homeomorphisms, Energy-minimal deformations, Harmonic mappings, P-harmonic equation, Variational integrals",

author = "Tadeusz Iwaniec and Jani Onninen",

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year = "2017",

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AU - Iwaniec, Tadeusz

AU - Onninen, Jani

N1 - Publisher Copyright: © European Mathematical Society 2017.

PY - 2017

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N2 - Let X,Y R2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X onto → Y in the Sobolev space W 1,p(X,R2), p ≥ 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.

AB - Let X,Y R2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X onto → Y in the Sobolev space W 1,p(X,R2), p ≥ 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.

KW - Approximation of Sobolev homeomorphisms

KW - Energy-minimal deformations

KW - Harmonic mappings

KW - P-harmonic equation

KW - Variational integrals

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JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 2

ER -

Limits of Sobolev homeomorphisms

Abstract

Keywords

ASJC Scopus subject areas

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