Otar Chkadua and Roland Duduchava
abstract:
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.