Champs div-rot de distortion finie

Tadeusz Iwaniec; Carlo Sbordone

doi:10.1016/S0764-4442(98)80160-2

Champs div-rot de distortion finie

Translated title of the contribution: Div-curl fields of finite distortion

Tadeusz Iwaniec, Carlo Sbordone

Department of Mathematics

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

9 Scopus citations

Abstract

Regularity results for div-curl fields (B, E) ∈ L^q_loc (Ω, ℝⁿ × ℝⁿ), q>1, div B = 0, curl E = 0 of finite distortion K : Ω ⊂ ℝⁿ → [1, ∞), i.e. satisfying a.e. in Ω |B(x)|² + |E(x)|² ≤ (K(x) + K^-1 (x)) 〈B(x), E(x)〉, are given, in analogy with the theory of quasiconformal mappings in the plane. Almost optimal integrability theorems for the gradient of weak solutions to some linear and nonlinear pde's follow.

Translated title of the contribution	Div-curl fields of finite distortion
Original language	French
Pages (from-to)	729-734
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	327
Issue number	8
DOIs	https://doi.org/10.1016/S0764-4442(98)80160-2
State	Published - Oct 1998

ASJC Scopus subject areas

Mathematics(all)

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10.1016/S0764-4442(98)80160-2

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abstract = "Regularity results for div-curl fields (B, E) ∈ Lqloc (Ω, ℝn × ℝn), q>1, div B = 0, curl E = 0 of finite distortion K : Ω ⊂ ℝn → [1, ∞), i.e. satisfying a.e. in Ω |B(x)|2 + |E(x)|2 ≤ (K(x) + K-1 (x)) 〈B(x), E(x)〉, are given, in analogy with the theory of quasiconformal mappings in the plane. Almost optimal integrability theorems for the gradient of weak solutions to some linear and nonlinear pde's follow.",

author = "Tadeusz Iwaniec and Carlo Sbordone",

year = "1998",

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AB - Regularity results for div-curl fields (B, E) ∈ Lqloc (Ω, ℝn × ℝn), q>1, div B = 0, curl E = 0 of finite distortion K : Ω ⊂ ℝn → [1, ∞), i.e. satisfying a.e. in Ω |B(x)|2 + |E(x)|2 ≤ (K(x) + K-1 (x)) 〈B(x), E(x)〉, are given, in analogy with the theory of quasiconformal mappings in the plane. Almost optimal integrability theorems for the gradient of weak solutions to some linear and nonlinear pde's follow.

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Champs div-rot de distortion finie

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