Invited talk, Beijing University of Technology, Oct. 30, 2015.
Abstract. In this talk, I will show the a priori estimates of Sobolev norms for a free boundary problem of the incompressible neo-Hookean elastodynamics in two and three spatial dimensions by adopting a geometrical point of view of Christodoulou-Lindblad. Some estimates on the second fundamental form and velocity of the free surface are also obtained. This is based on a joint work with Professor D. Wang.