On Invertibility of Sobolev Mappings
Leonid V. Kovalev, Jani Onninen
TL;DR
This paper establishes conditions under which Sobolev solutions to specific differential inclusions are invertible, extending known results even for quasiregular mappings in two dimensions.
Contribution
It provides new invertibility results for Sobolev solutions of differential inclusions that restrict eigenvalues, applicable to quasiregular mappings in 2D.
Findings
Proved local invertibility of Sobolev solutions under certain conditions.
Established global invertibility for specific differential inclusions.
Extended invertibility results to quasiregular mappings in two dimensions.
Abstract
We prove local and global invertibility of Sobolev solutions of certain differential inclusions which prevent the differential matrix from having negative eigenvalues. Our results are new even for quasiregular mappings in two dimensions.
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