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MiS Preprint
42/2006
On the Regularity of a Free Boundary Near Contact Points With a Fixed Boundary
John Andersson
Abstract
We investigate the regularity of a free boundary near contact points with a fixed boundary, with $C^{1,1}$ boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly $C^1$ up to the fixed boundary. We will also construct some examples of irregular free boundaries.
