Limit of p-Laplacian Obstacle problems

In this paper we study asymptotic behavior of solutions of obstacle problems for $p-$Laplacians as $p\to \infty.$ For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of whole family of the solutions of obstacle problems either for data $f$ that change sign in $\Omega$ or for data $f$ (that do not change sign in $\Omega$) possibly vanishing in a set of positive measure

Reinforcement problems for variational inequalities on fractal sets

The aim of this paper is to study reinforcement problems for variational inequalities of the obstacle type on fractal sets

Weighted Estimates on fractal domains

The aim of the paper is to establish estimates in weighted Sobolev spaces for the solutions of the Dirichlet problems on snowflake domains, as well as uniform estimates for the solutions of the Dirichlet problems on pre-fractal approximating domains

Layered fractal fibers and potentials

We study spectral asymptotic properties of conductive layered-thin-fibers of invasive fractal nature. The problem is formulated as a boundary value problem for singular elliptic operators with potentials in a quasi-filling geometry for the fibers. The methods are those of variational singular homogenization and M-convergence. We prove that the spectral measures of the differential problems converge to the spectral measure of a non-trivial self-adjoint operator with fractal terms

Asymptotic analysis of singular problems in perforated cylinders.

In this paper, we deal with elliptic problems having terms singular in the variable uu which represents the solution. The problems are posed in cylinders Ωnε of height 2n and perforated according to a parameter ε. We study existence, uniqueness and asymptotic behavior of the solutions uεn as the cylinders become infinite (n→+∞) and the size of the holes decreases while the number of the holes increases (ε→0)

Transmission problems with highly conductive fractal layers

Second order transmission problems with fractal layers are studied. Existence, uniqueness, regularity results and asymptotic behaviour are discussed

Harnack inequalities for energy forms on fractal sets.

There is a huge literature about Harnack inequalities so here I restrict my talk to the case of weak solutions of elliptic equations in divergence form mentioning only fundamental contributions obtained by means of purely analytic tools and giving few historical references. I focus my attention on Harnack inequalities for either Dirichlet forms or p-homogeneous energy forms on fractal sets