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 , as well as in exact controllability problems. © 2000 Rocky Mountain Mathematics Consortium.
Rocky Mountain Journal of Mathematics
Lasiecka, I., & Triggiani, R. (2000). Sharp regularity theory for elastic and thermoelastic kirchoff equations with free boundary conditions. Rocky Mountain Journal of Mathematics, 30 (3), 981-1024. https://doi.org/10.1216/rmjm/1021477256