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 σ-harmonic mappings

Giovanni Alessandrini;
2020-01-01

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.
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https://lematematiche.dmi.unict.it/index.php/lematematiche/article/view/1964
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2957785
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