Inverse function theorems and Jacobians over metric spaces. (English) Zbl 1309.26015
Summary: We present inversion results for Lipschitz maps \(f : \Omega \subset \mathbb{R}^{N} \to (Y, d)\) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
MSC:
| 26B10 | Implicit function theorems, Jacobians, transformations with several variables |
| 26B15 | Integration of real functions of several variables: length, area, volume |
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
Keywords:
calculus of variations; geometric measure theory; area formula; lower semicontinuity; Jacobian; inversion theoremReferences:
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