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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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