Publication

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Xavier Fernandez-Real Girona
2021
Journal Articles

Abstract

We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. with infinite Hn−1 measure. The only two assumptions under which a nice structure result for degenerate points has been established are when φ is analytic, and when Δφ0. Finally, we construct some new examples of free boundaries with degenerate points.

Official source

https://infoscience.epfl.ch/entities/publication/72bf6a8f-cdae-4430-866b-66513329597c

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Free Boundary Regularity for Almost Every Solution to the Signorini Problem

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