Abstract
Given a two-dimensional mapping U whose components solve a divergence structure elliptic equation,we give necessary and sufficient conditions on the boundary so that U is a global diffeomorphism.
Highlights
IntroductionIn [4], the present authors investigated, in the case of harmonic mappings, which additional conditions are needed for invertibility in the case of a possibly non-convex target D
Let B = {(x, y) ∈ R2 ∶ x2 + y2 < 1} denote the unit disk
Given a diffeomorphism Φ = ( 1, 2) from the unit circle B onto a simple closed curve γ ⊆ R2, we denote by D the bounded domain such that D =
Summary
In [4], the present authors investigated, in the case of harmonic mappings, which additional conditions are needed for invertibility in the case of a possibly non-convex target D. In [4, Theorem 1.3] it is proven that, assuming = I , U is a diffeomorphism if and only if det DU > 0 everywhere on B. An improvement to this result, still in the harmonic case, is due to Kalaj [17].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
