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.
Translated title of the contribution | Div-curl fields of finite distortion |
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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 | |
State | Published - Oct 1998 |
ASJC Scopus subject areas
- Mathematics(all)