2013
DOI: 10.1080/17476933.2012.755755
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Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation

Abstract: International audienceWe study Hardy spaces $H^p_\nu$ of the conjugate Beltrami equation $\bar{\partial} f=\nu\bar{\partial f}$ over Dini-smooth finitely connected domains, for real contractive $\nu\in W^{1,r}$ with $r>2$, in the range $r/(r-1

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Cited by 16 publications
(49 citation statements)
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References 32 publications
(99 reference statements)
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“…If µ ≡ 0 then G = (Id − ν C)F , that is, F = G − νG 1 − |ν| 2 ∈ W 1,s c ( C ). This reinforces the fact already observed in [7] that the study of the regularity in the conjugate Beltrami equation is easier than in the complex Beltrami equation.…”
Section: Distributional Solutions Are True Solutionssupporting
confidence: 90%
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“…If µ ≡ 0 then G = (Id − ν C)F , that is, F = G − νG 1 − |ν| 2 ∈ W 1,s c ( C ). This reinforces the fact already observed in [7] that the study of the regularity in the conjugate Beltrami equation is easier than in the complex Beltrami equation.…”
Section: Distributional Solutions Are True Solutionssupporting
confidence: 90%
“…Such question for∂ f − µ ∂f was treated in detail in [9]. Later, in [7] interest arose in the counterparts for the distributional conjugate…”
Section: K+1mentioning
confidence: 99%
“…Condition (13) above means that (11) is strictly elliptic. Condition (12) is less restrictive than Lipschitz-regularity, but still it implies some Hölder-smoothness. Note that, since r > n, the space W 1,r (Ω) consists of multipliers on W 1,2 (Ω), see [58] (∂Ω), we may set ∂ n u = φ/σ ∈ W −1/2,2 R (∂Ω) and then it holds that…”
Section: The Conductivity Equationmentioning
confidence: 99%
“…Note that ν L ∞ (Ω) < 1 and that ν ∈ W 1,r R (Ω) because of (4), (12) and (13). Interior regularity estimates for (55) imply that f ∈ W 2,r loc (Ω) [12, Cor.…”
Section: Factorization and Regularitymentioning
confidence: 99%
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