Homogenization and concentrated capacity in reticular almost disconnected structuresHomogénéisation et capacité concentrée dans les structures réticulaires presque déconnectées

We compute the homogenized-concentrated limit for a pair of non-linearly coupled diffusion equations in a perforated cylindric domain with coaxial cylindric holes periodically distributed along its axis. This problem arises from visual transduction. To cite this article: D. Andreucci et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 329–332.     

A Wiener-type condition for boundary continuity of quasi-minima of variational integrals

A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral.     

On complemented copies of c 0 and ℓ ∞

We furnish examples of pairs of Banach spaces X, Y so that none of c ₀ and l _∞ live inside X ^? and Y, but they embed complementably into the space DP(X,Y) of the Dunford–Pettis operators from X into Y.     

A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

Harnack estimates for quasi-linear degenerate parabolic differential equations

We establish the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacian and porous medium type. It is shown that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy. The proof uses only measure-theoretical arguments, it reproduces the classical Moser theory, for non-degenerate equations, and it is novel even in that context. Hölder estimates are derived as a consequence of the Harnack inequality. The results solve a long standing problem in the theory of degenerate parabolic equations.