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.File in questo prodotto:
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