On weak minima of certain integral functionals
We prove a regularity result for weak minima of integral functionals of the form where F(x,ξ) is a Carathéodory function which grows as with some p > 1.
Su una convergenza di successioni di integrali del Calcolo delle Variazioni
A new kind of convergence for integrals of the Calculus of Variations was considered in [6], where a compactness theorem was given. Here, using some results of [4], we give a compactness result for a smaller class of functional possessing minima in Sobolev spaces, and deduce, by this convergence of integrals, the convergence of their minima and minimum points in suitable spaces.
On the homogenization of some nonlinear problems in perforated domains
Optimal -properties of Green’s functions for non-divergence elliptic equations in two dimensions
A sharp integrability result for non-negative adjoint solutions to planar non-divergence elliptic equations is proved. A uniform estimate is also given for the Green's function.
Linear elliptic equations with BMO coefficients
We prove an existence and uniqueness theorem for the Dirichlet problem for the equation in an open cube , when belongs to some , with close to 2. Here we assume that the coefficient belongs to the space BMO() of functions of bounded mean oscillation and verifies the condition for a.e. .
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