MiS Preprint Repository

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 ( 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

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.

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