Boundary regularity for a parabolic obstacle type problem
Summary: We study the regularity of the free boundary, near contact points with the fixed boundary, for a parabolic free boundary problem \[ \begin{alignedat}{2} \Delta u-\partial u/\partial t&= \chi_{\{u\neq 0\}} &\quad\text{in } &Q_r^+= \{(x,t)\in B_r\times (-r^2,0);\;x_1>0\},\\ u&= f(x,t) &\quad\text{on } &\{x_1=0\}\cap Q_r. \end{alignedat} \] We 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.
scientific article; zbMATH DE number 5819171