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MiS Preprint

The Free Boundary Near the Fixed Boundary for the Heat Equation

John Andersson


We study the regularity of the free boundary, near contact points with the fixed boundary, for a parabolic free boundary problem: \begin{displaymath} \begin{array}{ll} \Delta u-\frac{\partial u}{\partial t}=\chi_{\{u\ne 0\}} & \textrm{in } B_r^+. \end{array} \end{displaymath} We will show that the free boundary is a $C^1$ manifold up to the fixed boundary under certain regularity assumptions on the boundary data, the $C^1$ norm is uniform for a certain, and specified, subclass of solutions.

Apr 25, 2006
Apr 25, 2006
MSC Codes:
35K20, 35R35
Parabolic obstacle problem, boundary regularity

Related publications

2006 Repository Open Access
John Andersson

The free boundary near the fixed boundary for the heat equation