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 elastic Kirchoff equation with free boundary conditions (BC) and provide sharp trace and interior regularity results. The problem does not satisfy Lopatinski’s conditions. Pseudo-differential operator/micro-local analysis techniques are used. These results, in turn, yield a sharp regularity theory for the corresponding thermoelastic plate equation. The described sharp regularity theory, besides being of interest in itself, is critically needed in establishing a structural decomposition result of the corresponding thermoelastic semigroup with free BC [12], as well as in exact controllability problems. © 2000 Rocky Mountain Mathematics Consortium