On the Regularity of a Free Boundary Near Contact Points With a Fixed Boundary
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Submission date: 25. Apr. 2006
published in: Journal of differential equations, 232 (2007) 1, p. 285-302
DOI number (of the published article): 10.1016/j.jde.2006.06.012
MSC-Numbers: 35J25, 35R35
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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.