Study of partial differential equations appearing in continuum mechanics and utlization of mathematical softwares

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Main results obtained in the period are as follows :1.Korn-type inequalities for. vector fields tangent to the boundary have been studied. Important contributions are : (1) a class of singular domains on which Korn-type inequalities hold for vector fields tangent to the boundary has been proposed. (2) Korn-type inequalities for energy integral of isotropic elasticity with some degeneracy of strong convexity condition was investigated.2.A sufficient condition imposed on the coefficients for the static energy integral to be positive for vector-valued functions on any bounded Lipschitz domain was studied. Now the corresponding necessary condition is now being studied.3.Eigenvalue problem for the reduced wave equation of isotropic elasticity on a slab has been investigated in detail.4.We utilized the mathematical software "Mathematica" to realize Mobius band in Mathmatica' using narrow strip of flat paper with the aid of three slender circular cylinders.