Some variational results using generalizations of sequential lower semicontinuity.
Problema di Dirichlet e misto per equazioni ellittiche variazionali
I prove existence and unicity of the solution of Dirichlet's problem and a mixed problem for linear second order elliptic differential equations in divergence form, with discontinuous coefficients in an unbounded domain.
Problema al contorno misto per equazioni ellittiche di tipo variazionale su insiemi non limitati
I prove a theorem of existence and uniqueness for solutions of mixed boundary value problems for linear second order elliptic partial differential equations in divergence form with discontinuous coefficients.
Generalizations of Sequential Lower Semicontinuity
In [7] W.A. Kirk and L.M. Saliga and in [3] Y. Chen, Y.J. Cho and L. Yang introduced lower semicontinuity from above, a generalization of sequential lower semicontinuity, and they showed that well-known results, such as some sufficient conditions for the existence of minima, Ekeland's variational principle and Caristi's fixed point theorem, remain still true under lower semicontinuity from above. In the second of the above papers the authors also conjectured that, for convex functions on normed...
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