Displaying similar documents to “The harmonic and quasiconformal extension operators”

The Douady-Earle extension of quasihomographies

Ken-Ichi Sakan, Józef Zając (1996)

Banach Center Publications

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Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let A T ( K ) denote the family of all K-quasihomographies of T. With any f ∈ A T ( K ) we associate the Douady-Earle extension E f and give an explicit and asymptotically sharp estimate of the L ∞ norm of the complex dilatation of E f .

The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle

Dariusz Partyka (1995)

Banach Center Publications

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This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator A γ : ℍ → ℍ is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest...

Nonlinear analysis and quasiconformal mappings from the perspective of PDEs

Tadeusz Iwaniec (1999)

Banach Center Publications

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Contents Introduction 119 1. Quasiregular mappings 120 2. The Beltrami equation 121 3. The Beltrami-Dirac equation 122 4. A quest for compactness 124 5. Sharp L p -estimates versus variational integrals 125 6. Very weak solutions 128 7. Nonlinear commutators 129 8. Jacobians and wedge products 131 9. Degree formulas 134 References 136