Degenerate Weakly (k₁, k₂)-Quasiregular Mappings
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In this paper, we rst give the de nition of degenerate weakly (k₁, k₂)-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse Hölder inequality, we obtain the higher integrability result: for any q₁ satisfying [수식]there exists an integrable exponent p₁ = p1(n, l, k₁, k₂) > l, such that every degenerate weakly (k₁, k₂)-quasiregular mapping f∈W[수식] (Ω, Rⁿ) belongs to W[수식] (Ω, Rⁿ), that is, f is a degenerate (k₁, k₂)-quasiregular mapping in the usual sense.
Abstract
In this paper, we rst give the de nition of degenerate weakly (k₁, k₂)-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse Hölder inequality, we obtain the higher integrability result: for any q₁ satisfying [수식]there exists an integrable exponent p₁ = p1(n, l, k₁, k₂) > l, such that every degenerate weakly (k₁, k₂)-quasiregular mapping f∈W[수식] (Ω, Rⁿ) belongs to W[수식] (Ω, Rⁿ), that is, f is a degenerate (k₁, k₂)-quasiregular mapping in the usual sense.
참고문헌 (12)
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