Abstract: | Summary In this note, making use of a result of J. L. Lions, we examine some non linear elliptic variational inequalities defined
on domains which may be unbounded. Such variational inequalities are associated to a uniformely second order elliptic operator.
We start with the derivation of an existence theorem (on bounded domains) under non coerciveness assumptions. Next we examine
the convergence for the solutions of a collection of variational inequalities. To this purpose we study convergence theorems
for variational inequalities associated to operators belonging to a class of abstract mapping of pseudomonotone type between
Banach spaces. The solvability of some variational inequalities on unbounded domains then follows directly.
Entrata in Redazione il 6 aprile 1977.
Lavoro eseguito nell'ambito del C.N.R., Laboratorio per la Matematica Applicata via L. B. Alberti 4, Genova. |