A Priori Estimates for the Free Boundary Problem of Incompressible Neo-Hookean Elastodynamics

A free boundary problem for the incompressible neo-Hookean elastodynamics is studied in two and three spatial dimensions. The a priori estimates in Sobolev norms of solutions with the physical vacuum condition are established through a geometrical point of view. Some estimates on the second fundamental form and velocity of the free surface are also obtained.