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.
|Original language||English (US)|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - Oct 1998|
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