Boundary regularity for a parabolic obstacle type problem

John E. Andersson

doi:10.4171/ifb/235

JournalsifbVol. 12, No. 3pp. 279–291

Boundary regularity for a parabolic obstacle type problem

John E. Andersson
University of Warwick, Coventry, UK

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Abstract

We study the regularity of the free boundary, near contact points with the fixed boundary, for a parabolic free boundary problem

Δ u - \partial u / \partial t = χ_{{u \neq = 0}} u = f (x, t) in Q_{r}^{+} = {(x, t) \in B_{r} \times (- r^{2}, 0); x_{1} > 0}, on {x_{1} = 0} \cap Q_{r} .

We will show that under certain regularity assumptions on the boundary data $f$ the free boundary is a $C^{1}$ manifold up to the fixed boundary. We also show that the $C^{1}$ modulus of continuity is uniform for a certain, and specified, subclass of solutions.

Cite this article

John E. Andersson, Boundary regularity for a parabolic obstacle type problem. Interfaces Free Bound. 12 (2010), no. 3, pp. 279–291

DOI 10.4171/IFB/235