Higher order estimates for the curvature and nonlinear stability of stationary solutions for curvature flow with triple junction

We are interested in the motion of a network of three planar curves with a speed proportional to the curvature of the arcs, having perpendicular intersections with the outer boundary and a common intersection at a triple junction. We derive higher order energy estimates yielding a priori estimates for the H

References:

[1] H. Garcke, Y. Kohsaka and D. Sevcovic: Nonlinear stability of stationary solutions for curvature flow with triple junction, submitted. arXiv:0802.3036

[2] Ikota R. and Yanagida E.: A stability criterion for stationary curves to the curvature-driven motion with a triple junction, Differential Integral Equations 16 (2003), 707--726.