Abstract: | Summary We are concerned with non-variational boundary value problems, with omogeneus boundary conditions, for linear partial differential
equations of quasi-elliptic type in a bounded domain Θ in Rn.
It is well known that some of difficulties which arise in treating such problems, in comparison with ? regular ? elliptic
problems, are connected with the presence of angular points in Θ: let us point out withB. Pini 32] that ? a bounded domain for which it is possible to assign a correct boundary value problem for a quasi-elliptic but
not elliptic equation always has angular points ?.
We suppose Θ is a cartesian product of a finite number of open sets and, in order to overcome the difficulties attached to
the presence of angular points in Θ, taking as a model the two previous papers33], 34] devoted to elliptic problems with singular data, we investigate the problem within suitable Sobolev weight spaces, connected
with the angular points of Θ and included in the ones we have studied in35]. Within such spaces we get existence and uniqueness theorems.
Lavoro eseguito con contributo del C. N. R.
Entrata in Redazione il 30 ottobre 1971. |