Electron. J. Diff. Eqns., Vol. 1999(1999), No. 01, pp. 1-12.

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

Yoonmi Ham & Youngsang Ko

Abstract:
We study the regularity of a moving interface $x = \zeta (t)$ of the solutions for the initial value problem
$u_t = \left(|u_x|^{p-2}u_x \right)_x$
$u(x,0) =u_0 (x)$,
where $u_0\in L^1({\Bbb R})$ and $p greater than 2$. 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

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Yoonmi Ham
Department of Mathematics, Kyonggi University
Suwon, Kyonggi-do, 442-760, Korea
e-mail: ymham@kuic.kyonggi.ac.kr

Youngsang Ko
Department of Mathematics, Kyonggi University
Suwon, Kyonggi-do, 442-760, Korea
e-mail: ysgo@kuic.kyonggi.ac.kr

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