Barriers on cones for uniformly elliptic operators

Summary On every right circular cone and for every uniformly elliptic operator in nondivergence form there exists a barrier, that is, a supersolution which is zero at the vertex and positive elsewhere on the closed cone. These barriers are applied to the Dirichlet problem. Other applications are deferred to a later paper on ? extremal barriers ?

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Sommario Si considerano operatori uniformemente ellittici del secondo ordine, ma in forma di nondivergenza, a coefficienti misurabili in un cono circolare retto; si prova che esiste una funzione barriera, vale a dire una supersoluzione positiva nel cono chiuso eccettuato il vertice ove si annulla. Queste barriere sono impiegate per lo studio del problema di Dirichlet. Altre applicazioni sono rinviate ad una successiva pubblicazione su le ? barriere estremali ?.

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This work was supported by the Air Force Office of Scientific Research and the National Academy of Sciences through a Postdoctoral Research Fellowship for 1964–1965 at the University of Genova and also in the writeup stage by AFOSR grant number 553–64.