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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.

Received:
Apr 25, 2006
Published:
Apr 25, 2006
MSC Codes:
35J25, 35R35

Related publications

inJournal
2007 Repository Open Access
John Andersson

On the regularity of a free boundary near contact points with a fixed boundary

In: Journal of differential equations, 232 (2007) 1, pp. 285-302