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

Δu∂u/∂t = χ{u≠0} in Qr+ = {(x, t) ∈ Br x (–_r_2, 0); _x_1 > 0},

u = f(x, t) on {_x_1 = 0} ∩ Qr.

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