## Limit problems for plates surrounded by soft material.(English)Zbl 0624.73021

In this paper the authors consider the problem of a clamped elastic plate having a central part $$\Omega$$ surrounded by a narrow annulus $$\Sigma_{\epsilon}$$ which width $$r_{\epsilon}$$ as well as Young modulus $$E_{\epsilon}$$ tend to zero when $$\epsilon$$ goes to zero. The question is to find the limit problem when $$\epsilon$$ goes to zero and to study the convergence of the solution of the plate $${\bar \Omega}\cup \Sigma_{\epsilon}$$ to the solution of the limit problem.
For this purpose, the authors study a more general mathematical problem covering the case of the elastic plates. By using the tool of the $$\Gamma$$-convergence they find the limit problem and prove an interesting convergence result on it.
The application of this general result to the elastic plate problem described above gives a very interesting mechanical result. The limit problem ammounts to be a problem of a clamped plate or a simply supported plate or an elastically supported plate depending on the behaviour of $$E_{\epsilon}/r_{\epsilon}$$ when $$\epsilon$$ goes to zero.