We consider mappings U=(u1,u2), whose components solve an arbitrary elliptic equation in divergence form in dimension two, and whose respective Dirichlet data φ1,φ2 constitute the parametrization of a simple closed curve γ. We prove that, if the interior of the curve γ is not convex, then we can find a parametrization Φ=(φ1,φ2) such that the mapping U is not invertible.
Breaking through borders with $sigma$-harmonic mappings / Nesi, Vincenzo; Alessandrini, Giovanni. - In: LE MATEMATICHE. - ISSN 0373-3505. - Vol LXXV:No 1(2020), pp. 57-66. [10.4418/2020.75.1.3]
Breaking through borders with $sigma$-harmonic mappings.
Vincenzo Nesi;
2020
Abstract
We consider mappings U=(u1,u2), whose components solve an arbitrary elliptic equation in divergence form in dimension two, and whose respective Dirichlet data φ1,φ2 constitute the parametrization of a simple closed curve γ. We prove that, if the interior of the curve γ is not convex, then we can find a parametrization Φ=(φ1,φ2) such that the mapping U is not invertible.File allegati a questo prodotto
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