Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 01, pp. 1-12.
Title: C-infinity interfaces of solutions for one-dimensional parabolic
p-Laplacian equations
Authors: Yoonmi Ham (Kyonggi Univ., Korea)
Youngsang Ko (Kyonggi Univ., Korea)
Abstract:
We study the regularity of a moving interface $x = \zeta (t)$ of the
solutions for the initial value problem
$$
u_t = \left(|u_x|^{p-2}u_x \right)_x \quad u(x,0) =u_0 (x)\,,
$$
where $u_0\in L^1({\Bbb R})$ and $p>2$. We prove that each side of the
moving interface is $C^{\infty}$.
Submitted November 11, 1998. Published January 5, 1999.
Math Subject Classification: 35K65
Key Words: p-Laplacian; free boundary; C-infinity regularity