# r-Regularity

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## Abstract

We provide a characterization of \(r\)-regular sets in terms of the Lipschitz regularity of normal vector fields to the boundary.

## Keywords

\(r\)-regularity Normal vector field \(C^1\)-boundary Lipschitz projection Euclidean distance## Mathematics Subject Classification

53B21 65D18## Notes

### Acknowledgments

Both authors would like to thank Armando P. Machado and Alessandro Margheri for valuable suggestions on the problems related to the Sturm–Liouville section. The first author was supported by “Fundação para a Ciência e a Tecnologia” through the Program POCI 2010 and the Project “Randomness in Deterministic Dynamical Systems and Applications” (PTDC-MAT-105448-2008). The second author was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Fundação para a Ciência e a Tecnologia”, through the Project PEstOE/MAT/UI0013/2014.

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