6533b851fe1ef96bd12a99b8
RESEARCH PRODUCT
Manifolds of quasiconformal mappings and the nonlinear Beltrami equation
Daniel FaracoDaniel FaracoJarmo JääskeläinenJarmo JääskeläinenJarmo JääskeläinenAlbert ClopKari Astalasubject
Pure mathematicsGeneral MathematicseducationMathematics::Analysis of PDEs01 natural sciencesBeltrami equationfunktioteoriaMathematics - Analysis of PDEsFOS: Mathematics0101 mathematicsComplex Variables (math.CV)30C62 (Primary) 35J60 35J46 (Secondary)MathematicsosittaisdifferentiaaliyhtälötPartial differential equationFunctional analysisMathematics - Complex Variables010102 general mathematicsStructure functionMathematics::Spectral Theory16. Peace & justiceManifold010101 applied mathematicsNonlinear systemmonistotAnalysisAnalysis of PDEs (math.AP)description
In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$ generate a two-dimensional manifold of quasiconformal mappings $\mathcal{F}_{\mathcal{H}} \subset W^{1,2}_{\mathrm{loc}}(\mathbb{C})$. Moreover, we show that under regularity assumptions on $\mathcal{H}$, the manifold $\mathcal{F}_{\mathcal{H}}$ defines the structure function $\mathcal{H}$ uniquely.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-12-12 |