Abstract
We give a generalization of a known theorem from classical complex analysis, namely the univalence on the boundary theorem. We apply this result to obtain some univalence conditions for Sobolev mappings \(f\in C({\overline{D}},{\mathbb {R}}^n)\bigcap W_{loc}^{1,q}(D,{\mathbb {R}}^n)\) which are injective on \(\partial D\), in connection with a known result of Ball from (Proc R Soc Edinb Sect A 88(3–4):315–328, 1981) modeling nonlinear elasticity.
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Communicated by Heinrich Begehr.
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Cristea, M. A Generalization of the Univalence on the Boundary Theorem with Applications to Sobolev Mappings. Complex Anal. Oper. Theory 11, 1789–1799 (2017). https://doi.org/10.1007/s11785-017-0703-3
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DOI: https://doi.org/10.1007/s11785-017-0703-3
Keywords
- Generalization of the univalence on the boundary theorem
- Univalence theorems for Sobolev mappings
- Openness and discreteness results for Sobolev mappings