Operatori ellittici massiminimanti
Abstract
In the theory of second order elliptic equations, in non divergence form, two non linear elliptic operators, which are non convex with respect to the second derivatives, are studied. Such operators are called maximinimal because of their extremal properties and they are a generalization of the extremal elliptic operators in [7]. They can be used to study eigenvalues of elliptic equations, corresponding to eigenfunctions with changes of sign. In this work the Dirichlet problem for these operators in studied. A nonuniqueness example, in dimension m ≥ 2, is costrued and a nonexistence theorem in W^{2,m}, m ≥ 3, is proved.
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