H1-estimates of Jacobians by subdeterminants

Tadeusz Iwaniec; Jani Onninen

doi:10.1007/s00208-002-0341-5

H¹-estimates of Jacobians by subdeterminants

Tadeusz Iwaniec, Jani Onninen

Department of Mathematics

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

45 Scopus citations

Abstract

Let f : Ω → ℝⁿ be a mapping in the Sobolev space, W_loc^1,n-1 (Ω, ℝⁿ), n ≥ 2. We assume that the cofactors of the differential matrix Df (x) belong to L^n/n-1 (Ω). Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space H¹ (Ω).

Original language	English (US)
Pages (from-to)	341-358
Number of pages	18
Journal	Mathematische Annalen
Volume	324
Issue number	2
DOIs	https://doi.org/10.1007/s00208-002-0341-5
State	Published - 2002

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-002-0341-5

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abstract = "Let f : Ω → ℝn be a mapping in the Sobolev space, Wloc1,n-1 (Ω, ℝn), n ≥ 2. We assume that the cofactors of the differential matrix Df (x) belong to Ln/n-1 (Ω). Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space H1 (Ω).",

author = "Tadeusz Iwaniec and Jani Onninen",

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AB - Let f : Ω → ℝn be a mapping in the Sobolev space, Wloc1,n-1 (Ω, ℝn), n ≥ 2. We assume that the cofactors of the differential matrix Df (x) belong to Ln/n-1 (Ω). Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space H1 (Ω).

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H¹-estimates of Jacobians by subdeterminants

Abstract

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