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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 C1,1 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 C1 up to the fixed boundary. We will also construct some examples of irregular free boundaries.

Received:
25.04.06
Published:
25.04.06
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