C-infinity interfaces of solutions for one-dimensional parabolic p-Laplacian equations

Abstract

We study the regularity of a moving interface $x = zeta (t)$ of the solutions for the initial value problem $$ u_t = left(|u_x|^{p-2}u_x ight)_x quad u(x,0) =u_0 (x),, $$ where $u_0in L^1({Bbb R})$ and $p>2$. We prove that each side of the moving interface is $C^{infty}$.

Keywords

• p-Laplacian
• free boundary
• C-infinity regularity