Otar Chkadua and Roland Duduchava

Asymptotics of Solutions to Some Boundary Value Problems of Elasticity for Bodies with Cuspidal Edges

The main purpose of the paper is to obtain complete asymptotic expansion of solutions to boundary value problems of elasticity of Dirichlet, Neumann and mixed type for an $n$-dimensional $(n\geq 2)$ composed body in $\bR^n$. The body is composed of two anisotropic bodies with smooth boundaries stick together along parts of their boundaries. Therefore the body has a closed smooth cuspidal edge, along which the Dirichlet and Neumann conditions in the mixed problem collide. Asymptotics of solutions are obtained near the cuspidal edge ($L_p$--theory), with precise description of exponents and of logarithmic terms of the expansion.

Mathematics Subject Classification: 47A68, 35J25, 35J55.

Key words and phrases: Dirichlet, Neumann and mixed problems, anisotropic homogeneous media, pseudodifferential operators, asymptotic of solutions, Wiener-Hopf method.