Degeneration of semielliptic equations with constant coefficients in rectangular parallelepipeds

The paper gives a description of an algorithm of asymptotic expansion in E > (E > > 0) of the solution u (E >) of the Dirichlet problem for the linear differential semielliptic equation L (E >) u (E >) = h in rectangular parallelepipeds, which contains higher derivatives with a small parameter E >. The algorithm is based on the solution of the degenerating as E > -> 0 Dirichlet problem for the semielliptic equation L (0) u = h of lower order. Some theorems on uniform solvability and regular degeneracy are proved.