On the Regularity of a Free Boundary Near Contact Points With a Fixed Boundary

John Andersson
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Submission date: 25. Apr. 2006
Pages: 21
MSC-Numbers: 35J25, 35R35
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Abstract:
We investigate the regularity of a free boundary near contact points with a fixed boundary, with 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 up to the fixed boundary. We will also construct some examples of irregular free boundaries.