The Free Boundary Near the Fixed Boundary for the Heat Equation
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Submission date: 25. Apr. 2006
MSC-Numbers: 35K20, 35R35
Keywords and phrases: Parabolic obstacle problem, boundary regularity
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We study the regularity of the free boundary, near contact points with the fixed boundary, for a parabolic free boundary problem:
We will show that the free boundary is a manifold up to the fixed boundary under certain regularity assumptions on the boundary data, the norm is uniform for a certain, and specified, subclass of solutions.