arXiv subjects
Publications and source records attributed to JiGuang Bao.
We establish upper bounds on the blow-up rate of the gradients of solutions of the Lamé system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero.
It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.
By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Dirichlet problem of the degenerate elliptic equation $$ -|\nabla v|(\mathrm{div}(\frac{\nabla v}{|\nabla v|})+ν)=0 $$ is solvable in viscosity sense.