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Sharp regularity theory for elastic and thermoelastic Kirchhoff equations with free boundary conditions. (English) Zbl 0983.35032

The paper deals with a two-dimensional model of an elastic Kirchhoff equation with free boundary conditions. The authors used pseudo-differential technique, more precisely microlocal analysis technique, to obtain sharp trace and interior regularity results. Note that the equation under consideration does not satisfy Shapiro-Lopatinsky’s conditions. The obtained results can be applied to exact controllability problems as well.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35L55 Higher-order hyperbolic systems
35L70 Second-order nonlinear hyperbolic equations
35R35 Free boundary problems for PDEs
74F05 Thermal effects in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
93B05 Controllability
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References:

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