An Aronsson type approach to extremal quasiconformal mappings. (English) Zbl 1291.30145
Summary: We study \(C^{2}\) extremal quasiconformal mappings in space and establish necessary and sufficient conditions for a ‘localized’ form of extremality in the spirit of the work of G. Aronsson on absolutely minimizing Lipschitz extensions. We also prove short-time existence for smooth solutions of a gradient flow of QC diffeomorphisms associated to the extremal problem.
MSC:
| 30C70 | Extremal problems for conformal and quasiconformal mappings, variational methods |
| 30C75 | Extremal problems for conformal and quasiconformal mappings, other methods |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
Keywords:
extremal quasiconformal mappings; quasiconformal mappings in \(\mathbb R^{n}\); flow of diffeomorphisms; trace dilationReferences:
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