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Paper   IPM / M / 16497
School of Mathematics
  Title:   The distance function from the boundary of a domain with corners
  Author(s):  Mohammad Safdari
  Status:   Published
  Journal: Nonlinear Anal.
  Vol.:  181
  Year:  2019
  Pages:   294-310
  Supported by:  IPM
We study the regularity of the distance function to the boundary of a domain in R2, with respect to some asymmetric norms. We allow the boundary of the domain to have corners. We obtain an explicit formula for the second derivative of these distance functions. Furthermore, we study a generalized notion of the ridge of a domain, which is the set of singularities of a distance function to the boundary of the domain. We completely characterize the ridge by using a generalized notion of curvature.

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