Estimates of gradient and of Jacobian of harmonic mappings defined in the unit disk

DOI10.1090/S0002-9939-2010-10691-3zbMath1223.31001MaRDI QIDQ5200172

David Kalaj

Publication date: 1 August 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

harmonic functionPoisson integral

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (3)

Sobolev homeomorphic extensions ⋮ An embedding theorem for BV-functions ⋮ Recent studies on Sobolev mappings

Cites Work

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• \(L^p\)-integrability \& weak type \(L^{2}\)-estimates for the gradient of harmonic mappings of \(\mathbb D\)
• On quasiconformal self-mappings of the unit disk satisfying Poisson’s equation
• Lipschitz spaces and harmonic mappings
• Harmonic homeomorphisms of the closed disc to itself need be in $W^\{1,p\}$, $p<2$, but not $W^\{1,2\}$
• Extremal mappings of finite distortion

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