具源函数的p-Laplacian发展方程边界连续性

The Continuity of Free Boundary to the p-Laplacian Equation with Nonlinear Source

考虑退化方程ut=div(|u|p-2 u)+uq的Cauchy问题,其中初始函数u0(x)的支集有界,p>2,1<q<p-1,最大存在时间0<T<∞.用以研究带有热源项的支集边界的正则性;并通过构造逼近解序列的办法,利用比较原理证明了解u的自由边界关于空间变量x是Lipschitz连续的;进一步地,如果对u0(x)和非线性指标q做额外的假设,可以证明自由边界关于时间变量t也是局部Lipschitz连续的.

This paper is concerned with the Cauchy problem ut=div（｜△↓u｜p-z△↓u）＋uq, with initial u0 （x） has bounded compact support, p〉2,1〈q〈p-1, the most exist time 0〈T〈∞. This work establishes the regularity of the free boundary. By comparing with the constructed approximate sequence, the author proves that the boundary is Lip-continuous with space variables x,moreover, the boundary is local Lip-continuous with time variables t,provided that some assumptions on the initial data uo and q are made.