Sharp regularity theory for elastic and thermoelastic Kirchoff equations with free boundary conditions

We consider mixed problems for, initially, a two-dimensional model of an el astic Kirchoff equation with free boundary conditions (BC) and provide shar p trace and interior regularity results. The problem does not satisfy Lopat inski's conditions. Pseudo-differential operator/micro-local analysis techniques are used. Thes e results, in turn, yield a sharp regularity theory for the corresponding t hermoelastic plate equation. The described sharp regularity theory, besides being of interest in itself, is critically needed in establishing a struct ural decomposition result of the corresponding thermoelastic semigroup with free BC [12], as well as in exact controllability problems.