散度-旋度场的正则性及其应用

Abstract

Abstract:

The aim of the present paper is to prove higher integrability results for div-curl vector fields B, E)∈L_loc^q(1-ε)(Ω, Rⁿ)×L_loc^p(1-ε) (Ω, Rⁿ) , 1< p, q <∞, 1/p + 1/q =1, ε sufficiently small, such that divB =0, E= 0 satisfying a reverse inequality of the type
| B |^q + | E |^p ≤C <B, E> + | F |^q,
with F ∈L^r(Ω, Rⁿ), r > q (1-ε) . Applications to the theory of weak quasiregular mappings and very weak solutions of nonhomogeneous A -harmonic equations
divA (x, \nabla u) = div F
are given.

Key words: Regularity, Div-curl vector field, Reverse H\"older inequality

CLC Number:

35J60

GAO Hong-Ya, HAN Xiao-Fan. Regularity Results for Div-Curl Fields and Applications[J].Acta mathematica scientia,Series A, 2011, 31(2): 378-386.

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Regularity Results for Div-Curl Fields and Applications

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