Jacobian of weak limits of Sobolev homeomorphisms

Stanislav Hencl; Jani Onninen

doi:10.1515/acv-2016-0005

Jacobian of weak limits of Sobolev homeomorphisms

Stanislav Hencl, Jani Onninen

Department of Mathematics

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

3 Scopus citations

Abstract

Let Ω be a domain in ℝⁿ, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms f_k : Ω → ℝⁿ with positive Jacobian determinants, J(x, f_k) > 0, converges weakly in W^1,p(Ω, ℝⁿ), for some p ≥ 1, to a mapping f. We show that J(x, f) ≥ 0 a.e. in Ω. Generalizations to higher dimensions are also given.

Original language	English (US)
Pages (from-to)	65-73
Number of pages	9
Journal	Advances in Calculus of Variations
Volume	11
Issue number	1
DOIs	https://doi.org/10.1515/acv-2016-0005
State	Published - Jan 1 2018

Keywords

Jacobian
Sobolev homeomorphism
weak limits

ASJC Scopus subject areas

Analysis
Applied Mathematics

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author = "Stanislav Hencl and Jani Onninen",

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AU - Onninen, Jani

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N2 - Let Ω be a domain in ℝn, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms fk : Ω → ℝn with positive Jacobian determinants, J(x, fk) > 0, converges weakly in W1,p(Ω, ℝn), for some p ≥ 1, to a mapping f. We show that J(x, f) ≥ 0 a.e. in Ω. Generalizations to higher dimensions are also given.

AB - Let Ω be a domain in ℝn, where n = 2, 3. Suppose that a sequence of Sobolev homeomorphisms fk : Ω → ℝn with positive Jacobian determinants, J(x, fk) > 0, converges weakly in W1,p(Ω, ℝn), for some p ≥ 1, to a mapping f. We show that J(x, f) ≥ 0 a.e. in Ω. Generalizations to higher dimensions are also given.

KW - Jacobian

KW - Sobolev homeomorphism

KW - weak limits

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JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

IS - 1

ER -

Jacobian of weak limits of Sobolev homeomorphisms

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Keywords

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