Mario Troisi

Equazioni ellittiche del secondo ordine di tipo non variazionale in aperti non limitati

SummaryIn this paper we study the Dirichlet problem, for second order, linear elliptic partial differential equations with discontinuous coefficients in unbounded domains. We obtain some results about existence and uniqueness of the solution in W2(Ω).

Spazi di Sobolev con peso e problemi ellittici in un angolo. - II

SummaryIn part I of this work (see [3]) Sobolev weight spaces related to boundary value problems for linear partial differential equations of elliptic type in a plane sector were discussed.This second part is concerned with such boundary value problems for homogeneous constant coefficient operators. They have been investigated within Sobolev weight spaces included in those previously discussed (see [3]). Existence and uniqueness theorems have been proved

Problemi al contorno con condizioni omogenee per le equazioni quasi-ellittiche

SummaryWe 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 papers[33], [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 in[35]. Within such spaces we get existence and uniqueness theorems.

Ulteriori contributi allo studio dei problemi ellittici in un angolo

SummaryIn[2] and[3] elliptic boundary value problems in a plane sector were investigated within certain Sobolev weight spaces Wrs1,s2 and W*rs1,s2 (see[1]), with the exception of some well-defined values of s1 − r + 1 and s2 − r + 1. This paper is concerned with such boundary value problems when s1 − r + 1 or s2 − r + 1 are exceptional values.